Theorem 19.28h 1454

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

Hypothesis

Ref	Expression
19.28h.1	|- ( ph -> A. x ph )

Assertion

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

Proof of Theorem 19.28h

Step	Hyp	Ref	Expression
1		19.26 1370	. 2 |- ( A. x ( ph /\ ps ) <-> ( A. x ph /\ A. x ps ) )
2		19.28h.1	. . . 4 |- ( ph -> A. x ph )
3	2	19.3h 1445	. . 3 |- ( A. x ph <-> ph )
4	3	anbi1i 431	. 2 |- ( ( A. x ph /\ A. x ps ) <-> ( ph /\ A. x ps ) )
5	1, 4	bitri 173	1 |- ( A. x ( ph /\ ps ) <-> ( ph /\ A. x ps ) )

Syntax hints:   -> wi 4   /\ wa 97   <-> wb 98   A.wal 1241

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-4 1400

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  nfan1  1456  aaanh  1478  exan  1583  19.28v  1780