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Theorem pm10.56 29762
Description: Theorem *10.56 in [WhiteheadRussell] p. 156. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
pm10.56  |-  ( ( A. x ( ph  ->  ps )  /\  E. x ( ph  /\  ch ) )  ->  E. x
( ps  /\  ch ) )

Proof of Theorem pm10.56
StepHypRef Expression
1 pm3.45 830 . . 3  |-  ( (
ph  ->  ps )  -> 
( ( ph  /\  ch )  ->  ( ps 
/\  ch ) ) )
21aleximi 1623 . 2  |-  ( A. x ( ph  ->  ps )  ->  ( E. x ( ph  /\  ch )  ->  E. x
( ps  /\  ch ) ) )
32imp 429 1  |-  ( ( A. x ( ph  ->  ps )  /\  E. x ( ph  /\  ch ) )  ->  E. x
( ps  /\  ch ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369   A.wal 1368   E.wex 1587
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588
This theorem is referenced by: (None)
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