Theorem 19.16 2017

Description: Theorem 19.16 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)

Hypothesis

Ref	Expression
19.16.1	|- F/ x ph

Assertion

Ref	Expression
19.16	|- ( A. x ( ph <-> ps ) -> ( ph <-> A. x ps ) )

Proof of Theorem 19.16

Step	Hyp	Ref	Expression
1		19.16.1	. . 3 |- F/ x ph
2	1	19.3 1943	. 2 |- ( A. x ph <-> ph )
3		albi 1684	. 2 |- ( A. x ( ph <-> ps ) -> ( A. x ph <-> A. x ps ) )
4	2, 3	syl5bbr 262	1 |- ( A. x ( ph <-> ps ) -> ( ph <-> A. x ps ) )

Syntax hints:   -> wi 4   <-> wb 187   A.wal 1435   F/wnf 1661

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-12 1909

This theorem depends on definitions:  df-bi 188  df-ex 1658  df-nf 1662

This theorem is referenced by: (None)