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Theorem aaanv 36142
Description: Theorem *11.56 in [WhiteheadRussell] p. 165. Special case of aaan 2003. (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 1728 . . 3  |-  F/ y
ph
2 nfv 1728 . . 3  |-  F/ x ps
31, 2aaan 2003 . 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 367   A.wal 1403
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-11 1866  ax-12 1878
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1634  df-nf 1638
This theorem is referenced by: (None)
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