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Theorem pm11.12 31524
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 31507 . . 3  |-  ( A. y ( ph  \/  ps )  ->  ( ph  \/  A. y ps )
)
21alimi 1638 . 2  |-  ( A. x A. y ( ph  \/  ps )  ->  A. x
( ph  \/  A. y ps ) )
3 pm10.12 31507 . 2  |-  ( A. x ( ph  \/  A. y ps )  -> 
( ph  \/  A. x A. y ps ) )
42, 3syl 16 1  |-  ( A. x A. y ( ph  \/  ps )  ->  ( ph  \/  A. x A. y ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \/ wo 366   A.wal 1396
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709
This theorem depends on definitions:  df-bi 185  df-or 368  df-ex 1618
This theorem is referenced by: (None)
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