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Theorem 19.23vv 2023
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 2022 . . 3  |-  ( A. y ( ph  ->  ps )  <->  ( E. y ph  ->  ps ) )
21albii 1554 . 2  |-  ( A. x A. y ( ph  ->  ps )  <->  A. x
( E. y ph  ->  ps ) )
3 19.23v 2022 . 2  |-  ( A. x ( E. y ph  ->  ps )  <->  ( E. x E. y ph  ->  ps ) )
42, 3bitri 242 1  |-  ( A. x A. y ( ph  ->  ps )  <->  ( E. x E. y ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178   A.wal 1532   E.wex 1537
This theorem is referenced by:  ssrel  4750  ssrelrel  4761  raliunxp  4799  bnj1052  28038  bnj1030  28050
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-17 1628  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540
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