Theorem hmphtop1

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	hmphtop1	$$⊢J\simeq K\to J\in \mathrm{Top}$$

Proof

Step	Hyp	Ref	Expression
1		hmphtop	$$⊢J\simeq K\to \left(J\in \mathrm{Top}\wedge K\in \mathrm{Top}\right)$$
2	1	simpld	$$⊢J\simeq K\to J\in \mathrm{Top}$$