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Theorem 19.21-2 1772
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 1771 . . 3  |-  ( A. y ( ph  ->  ps )  <->  ( ph  ->  A. y ps ) )
32albii 1554 . 2  |-  ( A. x A. y ( ph  ->  ps )  <->  A. x
( ph  ->  A. y ps ) )
4 19.21-2.1 . . 3  |-  F/ x ph
5419.21 1771 . 2  |-  ( A. x ( ph  ->  A. y ps )  <->  ( ph  ->  A. x A. y ps ) )
63, 5bitri 242 1  |-  ( A. x A. y ( ph  ->  ps )  <->  ( ph  ->  A. x A. y ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178   A.wal 1532   F/wnf 1539
This theorem is referenced by:  2eu6  2203  dford4  26490
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-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-nf 1540
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