Users' Mathboxes Mathbox for Andrew Salmon < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  pm10.12 Unicode version

Theorem pm10.12 27656
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 1609 . . 3  |-  F/ x ph
2119.32 1823 . 2  |-  ( A. x ( ph  \/  ps )  <->  ( ph  \/  A. x ps ) )
32biimpi 186 1  |-  ( A. x ( ph  \/  ps )  ->  ( ph  \/  A. x ps )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 357   A.wal 1530
This theorem is referenced by:  pm11.12  27674
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-nf 1535
  Copyright terms: Public domain W3C validator