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Theorem 19.23vv 1812
Description: Theorem 19.23 of [Margaris] p. 90 extended to two variables. (Contributed by NM, 10-Aug-2004.)
Assertion
Ref Expression
19.23vv  |-  ( A. x A. y ( ph  ->  ps )  <->  ( E. x E. y ph  ->  ps ) )
Distinct variable groups:    ps, x    ps, y
Allowed substitution hints:    ph( x, y)

Proof of Theorem 19.23vv
StepHypRef Expression
1 19.23v 1811 . . 3  |-  ( A. y ( ph  ->  ps )  <->  ( E. y ph  ->  ps ) )
21albii 1404 . 2  |-  ( A. x A. y ( ph  ->  ps )  <->  A. x
( E. y ph  ->  ps ) )
3 19.23v 1811 . 2  |-  ( A. x ( E. y ph  ->  ps )  <->  ( E. x E. y ph  ->  ps ) )
42, 3bitri 182 1  |-  ( A. x A. y ( ph  ->  ps )  <->  ( E. x E. y ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   A.wal 1287   E.wex 1426
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie2 1428  ax-17 1464
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  ssrel  4526  ssrelrel  4538  raliunxp  4577
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