Theorem 19.27v

Description: Version of 19.27 with a disjoint variable condition, requiring fewer axioms. (Contributed by NM, 3-Jun-2004)

	Ref	Expression
Assertion	19.27v	|- ( A. x ( ph /\ ps ) <-> ( A. x ph /\ ps ) )

Proof

Step	Hyp	Ref	Expression
1		19.26	|- ( A. x ( ph /\ ps ) <-> ( A. x ph /\ A. x ps ) )
2		19.3v	|- ( A. x ps <-> ps )
3	2	anbi2i	|- ( ( A. x ph /\ A. x ps ) <-> ( A. x ph /\ ps ) )
4	1 3	bitri	|- ( A. x ( ph /\ ps ) <-> ( A. x ph /\ ps ) )