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Theorem pm10.12 36571
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 19.32v 1779 . 2  |-  ( A. x ( ph  \/  ps )  <->  ( ph  \/  A. x ps ) )
21biimpi 198 1  |-  ( A. x ( ph  \/  ps )  ->  ( ph  \/  A. x ps )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \/ wo 370   A.wal 1436
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749
This theorem depends on definitions:  df-bi 189  df-or 372  df-ex 1661
This theorem is referenced by:  pm11.12  36588
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