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Theorem aaanv 27587
Description: Theorem *11.56 in [WhiteheadRussell] p. 165. Special case of aaan 1825. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
aaanv  |-  ( ( A. x ph  /\  A. y ps )  <->  A. x A. y ( ph  /\  ps ) )
Distinct variable groups:    ph, y    ps, x
Allowed substitution hints:    ph( x)    ps( y)

Proof of Theorem aaanv
StepHypRef Expression
1 nfv 1605 . . 3  |-  F/ y
ph
2 nfv 1605 . . 3  |-  F/ x ps
31, 2aaan 1825 . 2  |-  ( A. x A. y ( ph  /\ 
ps )  <->  ( A. x ph  /\  A. y ps ) )
43bicomi 193 1  |-  ( ( A. x ph  /\  A. y ps )  <->  A. x A. y ( ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358   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-7 1708  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-an 360  df-nf 1532
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