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Theorem stdpc4-2 26937
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 1897 . . 3  |-  ( A. y ph  ->  [ w  /  y ] ph )
21alimi 1546 . 2  |-  ( A. x A. y ph  ->  A. x [ w  / 
y ] ph )
3 stdpc4 1897 . 2  |-  ( A. x [ w  /  y ] ph  ->  [ z  /  x ] [ w  /  y ] ph )
42, 3syl 17 1  |-  ( A. x A. y ph  ->  [ z  /  x ] [ w  /  y ] ph )
Colors of variables: wff set class
Syntax hints:    -> wi 6   A.wal 1532   [wsb 1883
This theorem is referenced by:  pm11.11  26938
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536  ax-9 1684  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-sb 1884
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