Theorem 19.17 1549

Description: Theorem 19.17 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)

Hypothesis

Ref	Expression
19.17.1	|- F/ x ps

Assertion

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

Proof of Theorem 19.17

Step	Hyp	Ref	Expression
1		albi 1461	. 2 |- ( A. x ( ph <-> ps ) -> ( A. x ph <-> A. x ps ) )
2		19.17.1	. . 3 |- F/ x ps
3	2	19.3 1547	. 2 |- ( A. x ps <-> ps )
4	1, 3	bitrdi 195	1 |- ( A. x ( ph <-> ps ) -> ( A. x ph <-> ps ) )

Syntax hints:   -> wi 4   <-> wb 104   A.wal 1346   F/wnf 1453

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 1440  ax-gen 1442  ax-4 1503

This theorem depends on definitions:  df-bi 116  df-nf 1454

This theorem is referenced by: (None)