Theorem 19.17 1567

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 1479	. 2 |- ( A. x ( ph <-> ps ) -> ( A. x ph <-> A. x ps ) )
2		19.17.1	. . 3 |- F/ x ps
3	2	19.3 1565	. 2 |- ( A. x ps <-> ps )
4	1, 3	bitrdi 196	1 |- ( A. x ( ph <-> ps ) -> ( A. x ph <-> ps ) )

Syntax hints:   -> wi 4   <-> wb 105   A.wal 1362   F/wnf 1471

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-4 1521

This theorem depends on definitions:  df-bi 117  df-nf 1472

This theorem is referenced by: (None)