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Theorem alrot3 1415
Description: Theorem *11.21 in [WhiteheadRussell] p. 160. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
alrot3  |-  ( A. x A. y A. z ph 
<-> 
A. y A. z A. x ph )

Proof of Theorem alrot3
StepHypRef Expression
1 alcom 1408 . 2  |-  ( A. x A. y A. z ph 
<-> 
A. y A. x A. z ph )
2 alcom 1408 . . 3  |-  ( A. x A. z ph  <->  A. z A. x ph )
32albii 1400 . 2  |-  ( A. y A. x A. z ph 
<-> 
A. y A. z A. x ph )
41, 3bitri 182 1  |-  ( A. x A. y A. z ph 
<-> 
A. y A. z A. x ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 103   A.wal 1283
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  alrot4  1416  raliunxp  4505  dff13  5439
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