Theorem chle0i

Description: No Hilbert closed subspace is smaller than zero. (Contributed by NM, 7-Apr-2001) (New usage is discouraged.)

	Ref	Expression
Hypothesis	ch0le.1	|- A e. CH
Assertion	chle0i	|- ( A C_ 0H <-> A = 0H )

Proof

Step	Hyp	Ref	Expression
1		ch0le.1	|- A e. CH
2		chle0	|- ( A e. CH -> ( A C_ 0H <-> A = 0H ) )
3	1 2	ax-mp	|- ( A C_ 0H <-> A = 0H )