Theorem 19.28 1542

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 1457	. 2 |- ( A. x ( ph /\ ps ) <-> ( A. x ph /\ A. x ps ) )
2		19.28.1	. . . 4 |- F/ x ph
3	2	19.3 1533	. . 3 |- ( A. x ph <-> ph )
4	3	anbi1i 453	. 2 |- ( ( A. x ph /\ A. x ps ) <-> ( ph /\ A. x ps ) )
5	1, 4	bitri 183	1 |- ( A. x ( ph /\ ps ) <-> ( ph /\ A. x ps ) )

Syntax hints:   /\ wa 103   <-> wb 104   A.wal 1329   F/wnf 1436

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-4 1487

This theorem depends on definitions:  df-bi 116  df-nf 1437

This theorem is referenced by:  aaan  1566