Theorem r19.44zv

Description: Restricted version of Theorem 19.44 of Margaris p. 90. (Contributed by NM, 27-May-1998)

	Ref	Expression
Assertion	r19.44zv	|- ( A =/= (/) -> ( E. x e. A ( ph \/ ps ) <-> ( E. x e. A ph \/ ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		r19.43	|- ( E. x e. A ( ph \/ ps ) <-> ( E. x e. A ph \/ E. x e. A ps ) )
2		r19.9rzv	|- ( A =/= (/) -> ( ps <-> E. x e. A ps ) )
3	2	orbi2d	|- ( A =/= (/) -> ( ( E. x e. A ph \/ ps ) <-> ( E. x e. A ph \/ E. x e. A ps ) ) )
4	1 3	bitr4id	|- ( A =/= (/) -> ( E. x e. A ( ph \/ ps ) <-> ( E. x e. A ph \/ ps ) ) )