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Theorem pm10.14 27565
Description: Theorem *10.14 in [WhiteheadRussell] p. 146. (Contributed by Andrew Salmon, 17-Jun-2011.)
Assertion
Ref Expression
pm10.14  |-  ( ( A. x ph  /\  A. x ps )  -> 
( [ y  /  x ] ph  /\  [
y  /  x ] ps ) )

Proof of Theorem pm10.14
StepHypRef Expression
1 stdpc4 1966 . 2  |-  ( A. x ph  ->  [ y  /  x ] ph )
2 stdpc4 1966 . 2  |-  ( A. x ps  ->  [ y  /  x ] ps )
31, 2anim12i 549 1  |-  ( ( A. x ph  /\  A. x ps )  -> 
( [ y  /  x ] ph  /\  [
y  /  x ] ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   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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