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Theorem 19.21-2 1794
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 1793 . . 3  |-  ( A. y ( ph  ->  ps )  <->  ( ph  ->  A. y ps ) )
32albii 1555 . 2  |-  ( A. x A. y ( ph  ->  ps )  <->  A. x
( ph  ->  A. y ps ) )
4 19.21-2.1 . . 3  |-  F/ x ph
5419.21 1793 . 2  |-  ( A. x ( ph  ->  A. y ps )  <->  ( ph  ->  A. x A. y ps ) )
63, 5bitri 240 1  |-  ( A. x A. y ( ph  ->  ps )  <->  ( ph  ->  A. x A. y ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1529   F/wnf 1533
This theorem is referenced by:  2eu6  2230  dford4  27133
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-6 1705  ax-11 1717
This theorem depends on definitions:  df-bi 177  df-an 360  df-nf 1534
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