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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
StepHypRef Expression
1 biimp 197 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ph  ->  ps ) )
21al2imi 1689 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( A. x ph  ->  A. x ps )
)
3 biimpr 202 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ps  ->  ph ) )
43al2imi 1689 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( A. x ps 
->  A. x ph )
)
52, 4impbid 194 1  |-  ( A. x ( ph  <->  ps )  ->  ( A. x ph  <->  A. x ps ) )
Colors of variables: wff setvar class
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
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