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Theorem aaanv 30827
Description: Theorem *11.56 in [WhiteheadRussell] p. 165. Special case of aaan 1919. (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 1678 . . 3  |-  F/ y
ph
2 nfv 1678 . . 3  |-  F/ x ps
31, 2aaan 1919 . 2  |-  ( A. x A. y ( ph  /\ 
ps )  <->  ( A. x ph  /\  A. y ps ) )
43bicomi 202 1  |-  ( ( A. x ph  /\  A. y ps )  <->  A. x A. y ( ph  /\  ps ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 369   A.wal 1372
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-11 1786  ax-12 1798
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1592  df-nf 1595
This theorem is referenced by: (None)
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