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Theorem alrot4 1750
Description: Rotate 4 universal quantifiers twice. (Contributed by NM, 2-Feb-2005.) (Proof shortened by Fan Zheng, 6-Jun-2016.)
Assertion
Ref Expression
alrot4  |-  ( A. x A. y A. z A. w ph  <->  A. z A. w A. x A. y ph )

Proof of Theorem alrot4
StepHypRef Expression
1 alrot3 1749 . . 3  |-  ( A. y A. z A. w ph 
<-> 
A. z A. w A. y ph )
21albii 1572 . 2  |-  ( A. x A. y A. z A. w ph  <->  A. x A. z A. w A. y ph )
3 alrot3 1749 . 2  |-  ( A. x A. z A. w A. y ph  <->  A. z A. w A. x A. y ph )
42, 3bitri 241 1  |-  ( A. x A. y A. z A. w ph  <->  A. z A. w A. x A. y ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 177   A.wal 1546
This theorem is referenced by:  2mo  2340  fun11  5483
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-7 1745
This theorem depends on definitions:  df-bi 178
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