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Theorem alrot3 1784
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 1783 . 2  |-  ( A. x A. y A. z ph 
<-> 
A. y A. x A. z ph )
2 alcom 1783 . . 3  |-  ( A. x A. z ph  <->  A. z A. x ph )
32albii 1610 . 2  |-  ( A. y A. x A. z ph 
<-> 
A. y A. z A. x ph )
41, 3bitri 249 1  |-  ( A. x A. y A. z ph 
<-> 
A. y A. z A. x ph )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184   A.wal 1367
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-11 1780
This theorem depends on definitions:  df-bi 185
This theorem is referenced by:  alrot4  1785  nfnid  4520  raliunxp  4978  dff13  5970
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