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Theorem pm11.53v 1769
Description: Version of pm11.53 1988 with a dv condition, requiring fewer axioms. (Contributed by BJ, 7-Mar-2020.)
Assertion
Ref Expression
pm11.53v  |-  ( A. x A. y ( ph  ->  ps )  <->  ( E. x ph  ->  A. y ps ) )
Distinct variable groups:    ph, y    ps, x    x, y
Allowed substitution hints:    ph( x)    ps( y)

Proof of Theorem pm11.53v
StepHypRef Expression
1 19.21v 1734 . . 3  |-  ( A. y ( ph  ->  ps )  <->  ( ph  ->  A. y ps ) )
21albii 1645 . 2  |-  ( A. x A. y ( ph  ->  ps )  <->  A. x
( ph  ->  A. y ps ) )
3 19.23v 1765 . 2  |-  ( A. x ( ph  ->  A. y ps )  <->  ( E. x ph  ->  A. y ps ) )
42, 3bitri 249 1  |-  ( A. x A. y ( ph  ->  ps )  <->  ( E. x ph  ->  A. y ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   A.wal 1396   E.wex 1617
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752
This theorem depends on definitions:  df-bi 185  df-ex 1618
This theorem is referenced by:  sbnf2  2185
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