Theorem chseli

Description: Membership in subspace sum. (Contributed by NM, 19-Oct-1999) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ch0le.1	|- A e. CH
	chjcl.2	|- B e. CH
Assertion	chseli	|- ( C e. ( A +H B ) <-> E. x e. A E. y e. B C = ( x +h y ) )

Proof

Step	Hyp	Ref	Expression
1		ch0le.1	|- A e. CH
2		chjcl.2	|- B e. CH
3	1	chshii	|- A e. SH
4	2	chshii	|- B e. SH
5	3 4	shseli	|- ( C e. ( A +H B ) <-> E. x e. A E. y e. B C = ( x +h y ) )