diff --git a/mypy/typeops.py b/mypy/typeops.py
index 828791333f36..0833b15a0bee 100644
--- a/mypy/typeops.py
+++ b/mypy/typeops.py
@@ -604,10 +604,12 @@ def is_singleton_type(typ: Type) -> bool:
     constructing two distinct instances of 100001.
     """
     typ = get_proper_type(typ)
-    # TODO: Also make this return True if the type is a bool LiteralType.
+    # TODO:
     # Also make this return True if the type corresponds to ... (ellipsis) or NotImplemented?
     return (
-            isinstance(typ, NoneType) or (isinstance(typ, LiteralType) and typ.is_enum_literal())
+            isinstance(typ, NoneType)
+            or (isinstance(typ, LiteralType)
+                and (typ.is_enum_literal() or isinstance(typ.value, bool)))
             or (isinstance(typ, Instance) and typ.type.is_enum and len(get_enum_values(typ)) == 1)
     )
 
diff --git a/test-data/unit/check-narrowing.test b/test-data/unit/check-narrowing.test
index 45d4a625f8c7..a1d9685cc43d 100644
--- a/test-data/unit/check-narrowing.test
+++ b/test-data/unit/check-narrowing.test
@@ -984,3 +984,45 @@ if true_or_false:
 else:
     reveal_type(true_or_false)  # N: Revealed type is 'Literal[False]'
 [builtins fixtures/primitives.pyi]
+
+[case testNarrowingLiteralIdentityCheck]
+from typing import Union
+from typing_extensions import Literal
+
+str_or_false: Union[Literal[False], str]
+
+if str_or_false is not False:
+    reveal_type(str_or_false)   # N: Revealed type is 'builtins.str'
+else:
+    reveal_type(str_or_false)   # N: Revealed type is 'Literal[False]'
+
+if str_or_false is False:
+    reveal_type(str_or_false)  # N: Revealed type is 'Literal[False]'
+else:
+    reveal_type(str_or_false)  # N: Revealed type is 'builtins.str'
+
+str_or_true: Union[Literal[True], str]
+
+if str_or_true is True:
+    reveal_type(str_or_true)  # N: Revealed type is 'Literal[True]'
+else:
+    reveal_type(str_or_true)  # N: Revealed type is 'builtins.str'
+
+if str_or_true is not True:
+    reveal_type(str_or_true)  # N: Revealed type is 'builtins.str'
+else:
+    reveal_type(str_or_true)  # N: Revealed type is 'Literal[True]'
+
+str_or_bool_literal: Union[Literal[False], Literal[True], str]
+
+if str_or_bool_literal is not True:
+    reveal_type(str_or_bool_literal)  # N: Revealed type is 'Union[Literal[False], builtins.str]'
+else:
+    reveal_type(str_or_bool_literal)  # N: Revealed type is 'Literal[True]'
+
+if str_or_bool_literal is not True and str_or_bool_literal is not False:
+    reveal_type(str_or_bool_literal)  # N: Revealed type is 'builtins.str'
+else:
+    reveal_type(str_or_bool_literal)  # N: Revealed type is 'Union[Literal[False], Literal[True]]'
+
+[builtins fixtures/primitives.pyi]