Theorem albi 1692

Description: Theorem 19.15 of [Margaris] p. 90. (Contributed by NM, 24-Jan-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 197	. . 3 |- ( ( ph <-> ps ) -> ( ph -> ps ) )
2	1	al2imi 1689	. 2 |- ( A. x ( ph <-> ps ) -> ( A. x ph -> A. x ps ) )
3		biimpr 202	. . 3 |- ( ( ph <-> ps ) -> ( ps -> ph ) )
4	3	al2imi 1689	. 2 |- ( A. x ( ph <-> ps ) -> ( A. x ps -> A. x ph ) )
5	2, 4	impbid 194	1 |- ( A. x ( ph <-> ps ) -> ( A. x ph <-> A. x ps ) )

Syntax hints:   -> wi 4   <-> wb 188   A.wal 1444

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684

This theorem depends on definitions:  df-bi 189

This theorem is referenced by:  albii  1693  albidh  1728  19.16  2040  19.17  2041  equveli  2182  eqeq1d  2455  intmin4  4267  dfiin2g  4314  bj-2albi  31217  bj-hbxfrbi  31228  bj-nfbi  31229  wl-aleq  31880  2albi  36738  ralbidar  36809  sbcssOLD  36918  trsbcVD  37284  sbcssgVD  37290