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Theorem aaanOLD7 29700
Description: Rearrange universal quantifiers. (Contributed by NM, 12-Aug-1993.)
Hypotheses
Ref Expression
aaan.1OLD7  |-  F/ y
ph
aaan.2OLD7  |-  F/ x ps
Assertion
Ref Expression
aaanOLD7  |-  ( A. x A. y ( ph  /\ 
ps )  <->  ( A. x ph  /\  A. y ps ) )

Proof of Theorem aaanOLD7
StepHypRef Expression
1 aaan.1OLD7 . . . 4  |-  F/ y
ph
2119.28 1843 . . 3  |-  ( A. y ( ph  /\  ps )  <->  ( ph  /\  A. y ps ) )
32albii 1576 . 2  |-  ( A. x A. y ( ph  /\ 
ps )  <->  A. x
( ph  /\  A. y ps ) )
4 aaan.2OLD7 . . . 4  |-  F/ x ps
54nfalOLD7 29689 . . 3  |-  F/ x A. y ps
6519.27 1842 . 2  |-  ( A. x ( ph  /\  A. y ps )  <->  ( A. x ph  /\  A. y ps ) )
73, 6bitri 242 1  |-  ( A. x A. y ( ph  /\ 
ps )  <->  ( A. x ph  /\  A. y ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    /\ wa 360   A.wal 1550   F/wnf 1554
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-11 1762  ax-7OLD7 29680
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
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