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Theorem pm11.11 27581
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 27580 . . 3  |-  ( A. x A. y ph  ->  [ z  /  x ] [ w  /  y ] ph )
2 pm11.11.1 . . . 4  |-  ph
32ax-gen 1535 . . 3  |-  A. y ph
41, 3mpg 1537 . 2  |-  [ z  /  x ] [
w  /  y ]
ph
54gen2 1536 1  |-  A. z A. w [ z  /  x ] [ w  / 
y ] ph
Colors of variables: wff set class
Syntax hints:   A.wal 1529   [wsb 1631
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-6 1705  ax-7 1710  ax-11 1717  ax-12 1868
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1531  df-sb 1632
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