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Theorem albi 1573
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 179 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ph  ->  ps ) )
21al2imi 1570 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( A. x ph  ->  A. x ps )
)
3 bi2 190 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ps  ->  ph ) )
43al2imi 1570 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( A. x ps 
->  A. x ph )
)
52, 4impbid 184 1  |-  ( A. x ( ph  <->  ps )  ->  ( A. x ph  <->  A. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177   A.wal 1549
This theorem is referenced by:  albii  1575  albidh  1600  19.16  1883  19.17  1884  intmin4  4071  dfiin2g  4116  wl-aleq  26183  2albi  27491  ralbidar  27562  sbcssOLD  28482  trsbcVD  28843  sbcssVD  28849
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566
This theorem depends on definitions:  df-bi 178
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