Theorem albi 1461

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		biimp 117	. . 3 |- ( ( ph <-> ps ) -> ( ph -> ps ) )
2	1	al2imi 1451	. 2 |- ( A. x ( ph <-> ps ) -> ( A. x ph -> A. x ps ) )
3		biimpr 129	. . 3 |- ( ( ph <-> ps ) -> ( ps -> ph ) )
4	3	al2imi 1451	. 2 |- ( A. x ( ph <-> ps ) -> ( A. x ps -> A. x ph ) )
5	2, 4	impbid 128	1 |- ( A. x ( ph <-> ps ) -> ( A. x ph <-> A. x ps ) )

Syntax hints:   -> wi 4   <-> wb 104   A.wal 1346

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

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  albii  1463  albidh  1473  19.16  1548  19.17  1549  intmin4  3859  dfiin2g  3906