Theorem albi 1397

Description: Theorem 19.15 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem albi

Step	Hyp	Ref	Expression
1		bi1 116	. . 3 |- ( ( ph <-> ps ) -> ( ph -> ps ) )
2	1	al2imi 1387	. 2 |- ( A. x ( ph <-> ps ) -> ( A. x ph -> A. x ps ) )
3		bi2 128	. . 3 |- ( ( ph <-> ps ) -> ( ps -> ph ) )
4	3	al2imi 1387	. 2 |- ( A. x ( ph <-> ps ) -> ( A. x ps -> A. x ph ) )
5	2, 4	impbid 127	1 |- ( A. x ( ph <-> ps ) -> ( A. x ph <-> A. x ps ) )

Syntax hints:   -> wi 4   <-> wb 103   A.wal 1282

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  albii  1399  albidh  1409  19.16  1487  19.17  1488  intmin4  3664  dfiin2g  3711