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Theorem pm10.12 26719
Description: Theorem *10.12 in [WhiteheadRussell] p. 146. In *10, this is treated as an axiom, and the proofs in *10 are based on this theorem. (Contributed by Andrew Salmon, 17-Jun-2011.)
Assertion
Ref Expression
pm10.12  |-  ( A. x ( ph  \/  ps )  ->  ( ph  \/  A. x ps )
)
Distinct variable group:    ph, x
Allowed substitution hint:    ps( x)

Proof of Theorem pm10.12
StepHypRef Expression
1 nfv 1629 . . 3  |-  F/ x ph
2119.32 1794 . 2  |-  ( A. x ( ph  \/  ps )  <->  ( ph  \/  A. x ps ) )
32biimpi 188 1  |-  ( A. x ( ph  \/  ps )  ->  ( ph  \/  A. x ps )
)
Colors of variables: wff set class
Syntax hints:    -> wi 6    \/ wo 359   A.wal 1532
This theorem is referenced by:  pm11.12  26737
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-17 1628  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-nf 1540
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