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Metamath Proof Explorer

Theorem hmph

Description: Express the predicate J is homeomorphic to K . (Contributed by FL, 14-Feb-2007) (Revised by Mario Carneiro, 22-Aug-2015)

		Ref	Expression
	Assertion	hmph	$⊢ J ≃ K \leftrightarrow J Homeo K \neq \emptyset$

Step	Hyp	Ref	Expression
1		df-hmph	$⊢ ≃ = {Homeo}^{-1} [V ∖ 1_{𝑜}]$
2		hmeofn	$⊢ Homeo Fn (Top \times Top)$
3	1 2	brwitnlem	$⊢ J ≃ K \leftrightarrow J Homeo K \neq \emptyset$