Theorem 19.28 1500

Description: Theorem 19.28 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
19.28.1	|- F/ x ph

Assertion

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

Proof of Theorem 19.28

Step	Hyp	Ref	Expression
1		19.26 1415	. 2 |- ( A. x ( ph /\ ps ) <-> ( A. x ph /\ A. x ps ) )
2		19.28.1	. . . 4 |- F/ x ph
3	2	19.3 1491	. . 3 |- ( A. x ph <-> ph )
4	3	anbi1i 446	. 2 |- ( ( A. x ph /\ A. x ps ) <-> ( ph /\ A. x ps ) )
5	1, 4	bitri 182	1 |- ( A. x ( ph /\ ps ) <-> ( ph /\ A. x ps ) )

Syntax hints:   /\ wa 102   <-> wb 103   A.wal 1287   F/wnf 1394

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-4 1445

This theorem depends on definitions:  df-bi 115  df-nf 1395

This theorem is referenced by:  aaan  1524