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Theorem pm11.11 27549
Description: Theorem *11.11 in [WhiteheadRussell] p. 159. (Contributed by Andrew Salmon, 17-Jun-2011.)
Hypothesis
Ref Expression
pm11.11.1  |-  ph
Assertion
Ref Expression
pm11.11  |-  A. z A. w [ z  /  x ] [ w  / 
y ] ph

Proof of Theorem pm11.11
StepHypRef Expression
1 stdpc4-2 27548 . . 3  |-  ( A. x A. y ph  ->  [ z  /  x ] [ w  /  y ] ph )
2 pm11.11.1 . . . 4  |-  ph
32ax-gen 1556 . . 3  |-  A. y ph
41, 3mpg 1558 . 2  |-  [ z  /  x ] [
w  /  y ]
ph
54gen2 1557 1  |-  A. z A. w [ z  /  x ] [ w  / 
y ] ph
Colors of variables: wff set class
Syntax hints:   A.wal 1550   [wsb 1659
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762  ax-12 1951
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-sb 1660
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