Theorem 19.27 1575

Description: Theorem 19.27 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
19.27.1	|- F/ x ps

Assertion

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

Proof of Theorem 19.27

Step	Hyp	Ref	Expression
1		19.26 1495	. 2 |- ( A. x ( ph /\ ps ) <-> ( A. x ph /\ A. x ps ) )
2		19.27.1	. . . 4 |- F/ x ps
3	2	19.3 1568	. . 3 |- ( A. x ps <-> ps )
4	3	anbi2i 457	. 2 |- ( ( A. x ph /\ A. x ps ) <-> ( A. x ph /\ ps ) )
5	1, 4	bitri 184	1 |- ( A. x ( ph /\ ps ) <-> ( A. x ph /\ ps ) )

Syntax hints:   /\ wa 104   <-> wb 105   A.wal 1362   F/wnf 1474

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1461  ax-gen 1463  ax-4 1524

This theorem depends on definitions:  df-bi 117  df-nf 1475

This theorem is referenced by:  aaan  1601