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Theorem stdpc4-2 27580
Description: Theorem *11.1 in [WhiteheadRussell] p. 159. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
stdpc4-2  |-  ( A. x A. y ph  ->  [ z  /  x ] [ w  /  y ] ph )

Proof of Theorem stdpc4-2
StepHypRef Expression
1 stdpc4 1966 . . 3  |-  ( A. y ph  ->  [ w  /  y ] ph )
21alimi 1548 . 2  |-  ( A. x A. y ph  ->  A. x [ w  / 
y ] ph )
3 stdpc4 1966 . 2  |-  ( A. x [ w  /  y ] ph  ->  [ z  /  x ] [ w  /  y ] ph )
42, 3syl 15 1  |-  ( A. x A. y ph  ->  [ z  /  x ] [ w  /  y ] ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1529   [wsb 1631
This theorem is referenced by:  pm11.11  27581
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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