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Theorem aaanv 27566
Description: Theorem *11.56 in [WhiteheadRussell] p. 165. Special case of aaan 1907. (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 1630 . . 3  |-  F/ y
ph
2 nfv 1630 . . 3  |-  F/ x ps
31, 2aaan 1907 . 2  |-  ( A. x A. y ( ph  /\ 
ps )  <->  ( A. x ph  /\  A. y ps ) )
43bicomi 195 1  |-  ( ( A. x ph  /\  A. y ps )  <->  A. x A. y ( ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    /\ wa 360   A.wal 1550
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-7 1750  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
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