Users' Mathboxes Mathbox for Andrew Salmon < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  aaanv Unicode version

Theorem aaanv 26986
Description: Theorem *11.56 in [WhiteheadRussell] p. 165. Special case of aaan 1826. (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 1606 . . 3  |-  F/ y
ph
2 nfv 1606 . . 3  |-  F/ x ps
31, 2aaan 1826 . 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 1528
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-7 1709  ax-11 1716
This theorem depends on definitions:  df-bi 179  df-an 362  df-nf 1533
  Copyright terms: Public domain W3C validator