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Metamath Proof Explorer

Theorem chsh

Description: A closed subspace is a subspace. (Contributed by NM, 19-Oct-1999) (Revised by Mario Carneiro, 23-Dec-2013) (New usage is discouraged.)

		Ref	Expression
	Assertion	chsh	\|- ( H e. CH -> H e. SH )

Proof

Step	Hyp	Ref	Expression
1		isch	\|- ( H e. CH <-> ( H e. SH /\ ( ~~>v " ( H ^m NN ) ) C_ H ) )
2	1	simplbi	\|- ( H e. CH -> H e. SH )