Theorem r19.45zv

Description: Restricted version of Theorem 19.45 of Margaris p. 90. (Contributed by NM, 27-May-1998)

	Ref	Expression
Assertion	r19.45zv	|- ( A =/= (/) -> ( E. x e. A ( ph \/ ps ) <-> ( ph \/ E. x e. A ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		r19.9rzv	|- ( A =/= (/) -> ( ph <-> E. x e. A ph ) )
2	1	orbi1d	|- ( A =/= (/) -> ( ( ph \/ E. x e. A ps ) <-> ( E. x e. A ph \/ E. x e. A ps ) ) )
3		r19.43	|- ( E. x e. A ( ph \/ ps ) <-> ( E. x e. A ph \/ E. x e. A ps ) )
4	2 3	syl6rbbr	|- ( A =/= (/) -> ( E. x e. A ( ph \/ ps ) <-> ( ph \/ E. x e. A ps ) ) )