diff --git a/mypy/test/testtransform.py b/mypy/test/testtransform.py
index 803f2dcd4035..d884fe9137ab 100644
--- a/mypy/test/testtransform.py
+++ b/mypy/test/testtransform.py
@@ -60,6 +60,7 @@ def test_transform(testcase: DataDrivenTestCase) -> None:
                     and not os.path.splitext(
                         os.path.basename(f.path))[0].endswith('_')):
                 t = TypeAssertTransformVisitor()
+                t.test_only = True
                 f = t.mypyfile(f)
                 a += str(f).split('\n')
     except CompileError as e:
diff --git a/mypy/treetransform.py b/mypy/treetransform.py
index 4191569995b0..bd8a623455f7 100644
--- a/mypy/treetransform.py
+++ b/mypy/treetransform.py
@@ -20,7 +20,7 @@
     YieldFromExpr, NamedTupleExpr, TypedDictExpr, NonlocalDecl, SetComprehension,
     DictionaryComprehension, ComplexExpr, TypeAliasExpr, EllipsisExpr,
     YieldExpr, ExecStmt, Argument, BackquoteExpr, AwaitExpr, AssignmentExpr,
-    OverloadPart, EnumCallExpr, REVEAL_TYPE
+    OverloadPart, EnumCallExpr, REVEAL_TYPE, GDEF
 )
 from mypy.types import Type, FunctionLike, ProperType
 from mypy.traverser import TraverserVisitor
@@ -37,6 +37,8 @@ class TransformVisitor(NodeVisitor[Node]):
 
     Notes:
 
+     * This can only be used to transform functions or classes, not top-level
+       statements, and/or modules as a whole.
      * Do not duplicate TypeInfo nodes. This would generally not be desirable.
      * Only update some name binding cross-references, but only those that
        refer to Var, Decorator or FuncDef nodes, not those targeting ClassDef or
@@ -48,6 +50,9 @@ class TransformVisitor(NodeVisitor[Node]):
     """
 
     def __init__(self) -> None:
+        # To simplify testing, set this flag to True if you want to transform
+        # all statements in a file (this is prohibited in normal mode).
+        self.test_only = False
         # There may be multiple references to a Var node. Keep track of
         # Var translations using a dictionary.
         self.var_map = {}  # type: Dict[Var, Var]
@@ -58,6 +63,7 @@ def __init__(self) -> None:
         self.func_placeholder_map = {}  # type: Dict[FuncDef, FuncDef]
 
     def visit_mypy_file(self, node: MypyFile) -> MypyFile:
+        assert self.test_only, "This visitor should not be used for whole files."
         # NOTE: The 'names' and 'imports' instance variables will be empty!
         ignored_lines = {line: codes[:]
                          for line, codes in node.ignored_lines.items()}
@@ -358,7 +364,10 @@ def copy_ref(self, new: RefExpr, original: RefExpr) -> None:
         new.fullname = original.fullname
         target = original.node
         if isinstance(target, Var):
-            target = self.visit_var(target)
+            # Do not transform references to global variables. See
+            # testGenericFunctionAliasExpand for an example where this is important.
+            if original.kind != GDEF:
+                target = self.visit_var(target)
         elif isinstance(target, Decorator):
             target = self.visit_var(target.var)
         elif isinstance(target, FuncDef):
diff --git a/test-data/unit/check-generics.test b/test-data/unit/check-generics.test
index c4807c8fe1e7..654f33c590c2 100644
--- a/test-data/unit/check-generics.test
+++ b/test-data/unit/check-generics.test
@@ -2402,3 +2402,31 @@ def func(tp: Type[C[S]]) -> S:
     else:
         return reg[tp.test].test[0]
 [builtins fixtures/dict.pyi]
+
+[case testGenericFunctionAliasExpand]
+from typing import Optional, TypeVar
+
+T = TypeVar("T")
+def gen(x: T) -> T: ...
+gen_a = gen
+
+S = TypeVar("S", int, str)
+class C: ...
+def test() -> Optional[S]:
+    reveal_type(gen_a(C()))  # N: Revealed type is '__main__.C*'
+    return None
+
+[case testGenericFunctionMemberExpand]
+from typing import Optional, TypeVar, Callable
+
+T = TypeVar("T")
+
+class A:
+    def __init__(self) -> None:
+        self.gen: Callable[[T], T]
+
+S = TypeVar("S", int, str)
+class C: ...
+def test() -> Optional[S]:
+    reveal_type(A().gen(C()))  # N: Revealed type is '__main__.C*'
+    return None