diff --git a/pandas/core/common.py b/pandas/core/common.py
index 24680fc855b0d..cdcbc43055052 100644
--- a/pandas/core/common.py
+++ b/pandas/core/common.py
@@ -24,12 +24,7 @@
     is_extension_array_dtype,
     is_integer,
 )
-from pandas.core.dtypes.generic import (
-    ABCExtensionArray,
-    ABCIndex,
-    ABCIndexClass,
-    ABCSeries,
-)
+from pandas.core.dtypes.generic import ABCExtensionArray, ABCIndexClass, ABCSeries
 from pandas.core.dtypes.inference import iterable_not_string
 from pandas.core.dtypes.missing import isna, isnull, notnull  # noqa
 
@@ -105,7 +100,7 @@ def is_bool_indexer(key: Any) -> bool:
     check_array_indexer : Check that `key` is a valid array to index,
         and convert to an ndarray.
     """
-    if isinstance(key, (ABCSeries, np.ndarray, ABCIndex)) or (
+    if isinstance(key, (ABCSeries, np.ndarray, ABCIndexClass)) or (
         is_array_like(key) and is_extension_array_dtype(key.dtype)
     ):
         if key.dtype == np.object_:
@@ -471,7 +466,9 @@ def convert_to_list_like(
     Convert list-like or scalar input to list-like. List, numpy and pandas array-like
     inputs are returned unmodified whereas others are converted to list.
     """
-    if isinstance(values, (list, np.ndarray, ABCIndex, ABCSeries, ABCExtensionArray)):
+    if isinstance(
+        values, (list, np.ndarray, ABCIndexClass, ABCSeries, ABCExtensionArray)
+    ):
         # np.ndarray resolving as Any gives a false positive
         return values  # type: ignore[return-value]
     elif isinstance(values, abc.Iterable) and not isinstance(values, str):
diff --git a/pandas/core/dtypes/generic.py b/pandas/core/dtypes/generic.py
index 34891180906bb..0e5867809fe52 100644
--- a/pandas/core/dtypes/generic.py
+++ b/pandas/core/dtypes/generic.py
@@ -23,7 +23,6 @@ def _check(cls, inst) -> bool:
     return meta(name, tuple(), dct)
 
 
-ABCIndex = create_pandas_abc_type("ABCIndex", "_typ", ("index",))
 ABCInt64Index = create_pandas_abc_type("ABCInt64Index", "_typ", ("int64index",))
 ABCUInt64Index = create_pandas_abc_type("ABCUInt64Index", "_typ", ("uint64index",))
 ABCRangeIndex = create_pandas_abc_type("ABCRangeIndex", "_typ", ("rangeindex",))
diff --git a/pandas/core/indexes/datetimelike.py b/pandas/core/indexes/datetimelike.py
index 57f6a8ea0cca5..1b18f04ba603d 100644
--- a/pandas/core/indexes/datetimelike.py
+++ b/pandas/core/indexes/datetimelike.py
@@ -22,7 +22,7 @@
     is_scalar,
 )
 from pandas.core.dtypes.concat import concat_compat
-from pandas.core.dtypes.generic import ABCIndex, ABCSeries
+from pandas.core.dtypes.generic import ABCSeries
 
 from pandas.core.arrays import DatetimeArray, PeriodArray, TimedeltaArray
 from pandas.core.arrays.datetimelike import DatetimeLikeArrayMixin
@@ -53,16 +53,22 @@ def _join_i8_wrapper(joinf, with_indexers: bool = True):
     # error: 'staticmethod' used with a non-method
     @staticmethod  # type: ignore[misc]
     def wrapper(left, right):
-        if isinstance(left, (np.ndarray, ABCIndex, ABCSeries, DatetimeLikeArrayMixin)):
+        # Note: these only get called with left.dtype == right.dtype
+        if isinstance(
+            left, (np.ndarray, DatetimeIndexOpsMixin, ABCSeries, DatetimeLikeArrayMixin)
+        ):
             left = left.view("i8")
-        if isinstance(right, (np.ndarray, ABCIndex, ABCSeries, DatetimeLikeArrayMixin)):
+        if isinstance(
+            right,
+            (np.ndarray, DatetimeIndexOpsMixin, ABCSeries, DatetimeLikeArrayMixin),
+        ):
             right = right.view("i8")
 
         results = joinf(left, right)
         if with_indexers:
             # dtype should be timedelta64[ns] for TimedeltaIndex
             #  and datetime64[ns] for DatetimeIndex
-            dtype = left.dtype.base
+            dtype = cast(np.dtype, left.dtype).base
 
             join_index, left_indexer, right_indexer = results
             join_index = join_index.view(dtype)
diff --git a/pandas/core/ops/array_ops.py b/pandas/core/ops/array_ops.py
index 8142fc3e695a3..c855687552e82 100644
--- a/pandas/core/ops/array_ops.py
+++ b/pandas/core/ops/array_ops.py
@@ -27,7 +27,7 @@
     is_object_dtype,
     is_scalar,
 )
-from pandas.core.dtypes.generic import ABCExtensionArray, ABCIndex, ABCSeries
+from pandas.core.dtypes.generic import ABCExtensionArray, ABCIndexClass, ABCSeries
 from pandas.core.dtypes.missing import isna, notna
 
 from pandas.core.ops import missing
@@ -40,13 +40,11 @@ def comp_method_OBJECT_ARRAY(op, x, y):
     if isinstance(y, list):
         y = construct_1d_object_array_from_listlike(y)
 
-    if isinstance(y, (np.ndarray, ABCSeries, ABCIndex)):
-        # Note: these checks can be for ABCIndex and not ABCIndexClass
-        #  because that is the only object-dtype class.
+    if isinstance(y, (np.ndarray, ABCSeries, ABCIndexClass)):
         if not is_object_dtype(y.dtype):
             y = y.astype(np.object_)
 
-        if isinstance(y, (ABCSeries, ABCIndex)):
+        if isinstance(y, (ABCSeries, ABCIndexClass)):
             y = y._values
 
         if x.shape != y.shape:
diff --git a/pandas/tests/dtypes/test_generic.py b/pandas/tests/dtypes/test_generic.py
index e51b0546b0cee..847daa1e6b263 100644
--- a/pandas/tests/dtypes/test_generic.py
+++ b/pandas/tests/dtypes/test_generic.py
@@ -22,7 +22,6 @@ class TestABCClasses:
     timedelta_array = pd.core.arrays.TimedeltaArray(timedelta_index)
 
     def test_abc_types(self):
-        assert isinstance(pd.Index(["a", "b", "c"]), gt.ABCIndex)
         assert isinstance(pd.Int64Index([1, 2, 3]), gt.ABCInt64Index)
         assert isinstance(pd.UInt64Index([1, 2, 3]), gt.ABCUInt64Index)
         assert isinstance(pd.Float64Index([1, 2, 3]), gt.ABCFloat64Index)