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Theorem 19.21-2 1628
Description: Theorem 19.21 of [Margaris] p. 90 but with 2 quantifiers. (Contributed by NM, 4-Feb-2005.)
Hypotheses
Ref Expression
19.21-2.1  |-  F/ x ph
19.21-2.2  |-  F/ y
ph
Assertion
Ref Expression
19.21-2  |-  ( A. x A. y ( ph  ->  ps )  <->  ( ph  ->  A. x A. y ps ) )

Proof of Theorem 19.21-2
StepHypRef Expression
1 19.21-2.2 . . . 4  |-  F/ y
ph
2119.21 1545 . . 3  |-  ( A. y ( ph  ->  ps )  <->  ( ph  ->  A. y ps ) )
32albii 1429 . 2  |-  ( A. x A. y ( ph  ->  ps )  <->  A. x
( ph  ->  A. y ps ) )
4 19.21-2.1 . . 3  |-  F/ x ph
5419.21 1545 . 2  |-  ( A. x ( ph  ->  A. y ps )  <->  ( ph  ->  A. x A. y ps ) )
63, 5bitri 183 1  |-  ( A. x A. y ( ph  ->  ps )  <->  ( ph  ->  A. x A. y ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1312   F/wnf 1419
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408  ax-4 1470  ax-ial 1497  ax-i5r 1498
This theorem depends on definitions:  df-bi 116  df-nf 1420
This theorem is referenced by: (None)
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