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Theorem 19.21vv 27574
Description: Compare theorem *11.3 in [WhiteheadRussell] p. 161. Special case of theorem 19.21 of [Margaris] p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
19.21vv  |-  ( A. x A. y ( ps 
->  ph )  <->  ( ps  ->  A. x A. y ph ) )
Distinct variable groups:    ps, x    ps, y
Allowed substitution hints:    ph( x, y)

Proof of Theorem 19.21vv
StepHypRef Expression
1 19.21v 1831 . . 3  |-  ( A. y ( ps  ->  ph )  <->  ( ps  ->  A. y ph ) )
21albii 1553 . 2  |-  ( A. x A. y ( ps 
->  ph )  <->  A. x
( ps  ->  A. y ph ) )
3 19.21v 1831 . 2  |-  ( A. x ( ps  ->  A. y ph )  <->  ( ps  ->  A. x A. y ph ) )
42, 3bitri 240 1  |-  ( A. x A. y ( ps 
->  ph )  <->  ( ps  ->  A. x A. y ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1527
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-an 360  df-nf 1532
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