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Theorem pm11.12 26737
Description: Theorem *11.12 in [WhiteheadRussell] p. 159. (Contributed by Andrew Salmon, 17-Jun-2011.)
Assertion
Ref Expression
pm11.12  |-  ( A. x A. y ( ph  \/  ps )  ->  ( ph  \/  A. x A. y ps ) )
Distinct variable groups:    ph, x    ph, y
Allowed substitution hints:    ps( x, y)

Proof of Theorem pm11.12
StepHypRef Expression
1 pm10.12 26719 . . 3  |-  ( A. y ( ph  \/  ps )  ->  ( ph  \/  A. y ps )
)
21alimi 1546 . 2  |-  ( A. x A. y ( ph  \/  ps )  ->  A. x
( ph  \/  A. y ps ) )
3 pm10.12 26719 . 2  |-  ( A. x ( ph  \/  A. y ps )  -> 
( ph  \/  A. x A. y ps ) )
42, 3syl 17 1  |-  ( A. x A. y ( ph  \/  ps )  ->  ( ph  \/  A. x A. y ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    \/ wo 359   A.wal 1532
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-17 1628  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-nf 1540
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