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Theorem pm11.53g 24374
Description: Theorem *11.53 in [WhiteheadRussell] p. 164. (Contributed by FL, 27-Oct-2013.)
Hypotheses
Ref Expression
pm11.53g.1  |-  F/ y
ph
pm11.53g.2  |-  F/ x ps
Assertion
Ref Expression
pm11.53g  |-  ( A. x A. y ( ph  ->  ps )  <->  ( E. x ph  ->  A. y ps ) )

Proof of Theorem pm11.53g
StepHypRef Expression
1 pm11.53g.1 . . . 4  |-  F/ y
ph
2119.21 1793 . . 3  |-  ( A. y ( ph  ->  ps )  <->  ( ph  ->  A. y ps ) )
32albii 1553 . 2  |-  ( A. x A. y ( ph  ->  ps )  <->  A. x
( ph  ->  A. y ps ) )
4 pm11.53g.2 . . . 4  |-  F/ x ps
54nfal 1768 . . 3  |-  F/ x A. y ps
6519.23 1799 . 2  |-  ( A. x ( ph  ->  A. y ps )  <->  ( E. x ph  ->  A. y ps ) )
73, 6bitri 240 1  |-  ( A. x A. y ( ph  ->  ps )  <->  ( E. x ph  ->  A. y ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1527   E.wex 1528   F/wnf 1531
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1636  ax-8 1644  ax-6 1704  ax-7 1709  ax-11 1716
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532
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