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Theorem albi 1552
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
StepHypRef Expression
1 bi1 180 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ph  ->  ps ) )
21al2imi 1549 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( A. x ph  ->  A. x ps )
)
3 bi2 191 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ps  ->  ph ) )
43al2imi 1549 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( A. x ps 
->  A. x ph )
)
52, 4impbid 185 1  |-  ( A. x ( ph  <->  ps )  ->  ( A. x ph  <->  A. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178   A.wal 1528
This theorem is referenced by:  albii  1554  albidh  1578  19.16  1788  19.17  1789  intmin4  3892  dfiin2g  3937  2albi  26975  ralbidar  27047  sbcssOLD  27577  trsbcVD  27921  sbcssVD  27927
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545
This theorem depends on definitions:  df-bi 179
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