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Theorem 19.31vv 26981
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 1606 . . . 4  |-  F/ y ps
2119.31 1813 . . 3  |-  ( A. y ( ph  \/  ps )  <->  ( A. y ph  \/  ps ) )
32albii 1554 . 2  |-  ( A. x A. y ( ph  \/  ps )  <->  A. x
( A. y ph  \/  ps ) )
4 nfv 1606 . . 3  |-  F/ x ps
5419.31 1813 . 2  |-  ( A. x ( A. y ph  \/  ps )  <->  ( A. x A. y ph  \/  ps ) )
63, 5bitri 242 1  |-  ( A. x A. y ( ph  \/  ps )  <->  ( A. x A. y ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    \/ wo 359   A.wal 1528
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-6 1704  ax-11 1716
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1312  df-nf 1533
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