Theorem r19.27zv

Description: Restricted quantifier version of Theorem 19.27 of Margaris p. 90. It is valid only when the domain of quantification is not empty. (Contributed by NM, 19-Aug-2004)

	Ref	Expression
Assertion	r19.27zv	|- ( A =/= (/) -> ( A. x e. A ( ph /\ ps ) <-> ( A. x e. A ph /\ ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		nfv	|- F/ x ps
2	1	r19.27z	|- ( A =/= (/) -> ( A. x e. A ( ph /\ ps ) <-> ( A. x e. A ph /\ ps ) ) )