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Metamath Proof Explorer

Theorem hmeocnvcn

Description: The converse of a homeomorphism is continuous. (Contributed by Mario Carneiro, 22-Aug-2015)

		Ref	Expression
	Assertion	hmeocnvcn	$⊢ F \in (J Homeo K) \to F^{-1} \in (K Cn J)$

Step	Hyp	Ref	Expression
1		ishmeo	$⊢ F \in (J Homeo K) \leftrightarrow (F \in (J Cn K) \land F^{-1} \in (K Cn J))$
2	1	simprbi	$⊢ F \in (J Homeo K) \to F^{-1} \in (K Cn J)$