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Theorem pm10.542 26930
Description: Theorem *10.542 in [WhiteheadRussell] p. 156. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
pm10.542  |-  ( A. x ( ph  ->  ( ch  ->  ps )
)  <->  ( ch  ->  A. x ( ph  ->  ps ) ) )
Distinct variable group:    ch, x
Allowed substitution hints:    ph( x)    ps( x)

Proof of Theorem pm10.542
StepHypRef Expression
1 bi2.04 352 . . 3  |-  ( (
ph  ->  ( ch  ->  ps ) )  <->  ( ch  ->  ( ph  ->  ps ) ) )
21albii 1554 . 2  |-  ( A. x ( ph  ->  ( ch  ->  ps )
)  <->  A. x ( ch 
->  ( ph  ->  ps ) ) )
3 19.21v 2012 . 2  |-  ( A. x ( ch  ->  (
ph  ->  ps ) )  <-> 
( ch  ->  A. x
( ph  ->  ps )
) )
42, 3bitri 242 1  |-  ( A. x ( ph  ->  ( ch  ->  ps )
)  <->  ( ch  ->  A. x ( ph  ->  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178   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-an 362  df-nf 1540
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