Theorem albi 1746

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 205	. . 3 |- ( ( ph <-> ps ) -> ( ph -> ps ) )
2	1	al2imi 1743	. 2 |- ( A. x ( ph <-> ps ) -> ( A. x ph -> A. x ps ) )
3		biimpr 210	. . 3 |- ( ( ph <-> ps ) -> ( ps -> ph ) )
4	3	al2imi 1743	. 2 |- ( A. x ( ph <-> ps ) -> ( A. x ps -> A. x ph ) )
5	2, 4	impbid 202	1 |- ( A. x ( ph <-> ps ) -> ( A. x ph <-> A. x ps ) )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197

This theorem is referenced by:  albii  1747  nfbiit  1777  albidh  1793  19.16  2093  19.17  2094  equvel  2347  eqeq1d  2624  intmin4  4506  dfiin2g  4553  bj-2albi  32597  bj-hbxfrbi  32608  wl-aleq  33322  2albi  38577  ralbidar  38649  sbcssOLD  38756  trsbcVD  39113  sbcssgVD  39119