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Theorem albi 1551
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 178 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ph  ->  ps ) )
21al2imi 1548 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( A. x ph  ->  A. x ps )
)
3 bi2 189 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ps  ->  ph ) )
43al2imi 1548 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( A. x ps 
->  A. x ph )
)
52, 4impbid 183 1  |-  ( A. x ( ph  <->  ps )  ->  ( A. x ph  <->  A. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1527
This theorem is referenced by:  albii  1553  albidh  1577  19.16  1787  19.17  1788  intmin4  3891  dfiin2g  3936  2albi  27576  ralbidar  27648  sbcssOLD  28306  trsbcVD  28653  sbcssVD  28659
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544
This theorem depends on definitions:  df-bi 177
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