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Metamath Proof Explorer

Theorem hmeocn

Description: A homeomorphism is continuous. (Contributed by Mario Carneiro, 22-Aug-2015)

		Ref	Expression
	Assertion	hmeocn	$⊢ F \in (J Homeo K) \to F \in (J Cn K)$

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	simplbi	$⊢ F \in (J Homeo K) \to F \in (J Cn K)$