Theorem hmphtop2

Description: The relation "being homeomorphic to" implies the operands are topologies. (Contributed by FL, 23-Mar-2007) (Revised by Mario Carneiro, 23-Aug-2015)

	Ref	Expression
Assertion	hmphtop2	|- ( J ~= K -> K e. Top )

Proof

Step	Hyp	Ref	Expression
1		hmphtop	|- ( J ~= K -> ( J e. Top /\ K e. Top ) )
2	1	simprd	|- ( J ~= K -> K e. Top )