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Theorem alrot3 1462
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 1455 . 2  |-  ( A. x A. y A. z ph 
<-> 
A. y A. x A. z ph )
2 alcom 1455 . . 3  |-  ( A. x A. z ph  <->  A. z A. x ph )
32albii 1447 . 2  |-  ( A. y A. x A. z ph 
<-> 
A. y A. z A. x ph )
41, 3bitri 183 1  |-  ( A. x A. y A. z ph 
<-> 
A. y A. z A. x ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 104   A.wal 1330
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  alrot4  1463  raliunxp  4684  dff13  5673
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