Users' Mathboxes Mathbox for Andrew Salmon < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  19.31vv Unicode version

Theorem 19.31vv 26994
Description: Theorem *11.44 in [WhiteheadRussell] p. 163. Theorem 19.31 of [Margaris] p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
19.31vv  |-  ( A. x A. y ( ph  \/  ps )  <->  ( A. x A. y ph  \/  ps ) )
Distinct variable groups:    ps, x    ps, y
Allowed substitution hints:    ph( x, y)

Proof of Theorem 19.31vv
StepHypRef Expression
1 nfv 1605 . . . 4  |-  F/ y ps
2119.31 1812 . . 3  |-  ( A. y ( ph  \/  ps )  <->  ( A. y ph  \/  ps ) )
32albii 1553 . 2  |-  ( A. x A. y ( ph  \/  ps )  <->  A. x
( A. y ph  \/  ps ) )
4 nfv 1605 . . 3  |-  F/ x ps
5419.31 1812 . 2  |-  ( A. x ( A. y ph  \/  ps )  <->  ( A. x A. y ph  \/  ps ) )
63, 5bitri 240 1  |-  ( A. x A. y ( ph  \/  ps )  <->  ( A. x A. y ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    \/ wo 357   A.wal 1527
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-nf 1532
  Copyright terms: Public domain W3C validator