Theorem albi 1686

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 196	. . 3 |- ( ( ph <-> ps ) -> ( ph -> ps ) )
2	1	al2imi 1683	. 2 |- ( A. x ( ph <-> ps ) -> ( A. x ph -> A. x ps ) )
3		biimpr 201	. . 3 |- ( ( ph <-> ps ) -> ( ps -> ph ) )
4	3	al2imi 1683	. 2 |- ( A. x ( ph <-> ps ) -> ( A. x ps -> A. x ph ) )
5	2, 4	impbid 193	1 |- ( A. x ( ph <-> ps ) -> ( A. x ph <-> A. x ps ) )

Syntax hints:   -> wi 4   <-> wb 187   A.wal 1435

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678

This theorem depends on definitions:  df-bi 188

This theorem is referenced by:  albii  1687  albidh  1720  19.16  2013  19.17  2014  equveli  2143  eqeq1d  2424  intmin4  4282  dfiin2g  4329  bj-2albi  31192  bj-hbxfrbi  31203  bj-nfbi  31204  wl-aleq  31782  2albi  36585  ralbidar  36656  sbcssOLD  36765  trsbcVD  37135  sbcssgVD  37141