Theorem 19.28 1952

Description: Theorem 19.28 of [Margaris] p. 90. See 19.28v 1791 for a version requiring fewer axioms. (Contributed by NM, 1-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 1701	. 2 |- ( A. x ( ph /\ ps ) <-> ( A. x ph /\ A. x ps ) )
2		19.28.1	. . . 4 |- F/ x ph
3	2	19.3 1912	. . 3 |- ( A. x ph <-> ph )
4	3	anbi1i 693	. 2 |- ( ( A. x ph /\ A. x ps ) <-> ( ph /\ A. x ps ) )
5	1, 4	bitri 249	1 |- ( A. x ( ph /\ ps ) <-> ( ph /\ A. x ps ) )

Syntax hints:   <-> wb 184   /\ wa 367   A.wal 1403   F/wnf 1637

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-12 1878

This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1634  df-nf 1638

This theorem is referenced by:  nfan1  1955  aaan  2003  wl-ax11-lem7  31403