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Theorem alrot3 1610
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 1568 . 2  |-  ( A. x A. y A. z ph 
<-> 
A. y A. x A. z ph )
2 alcom 1568 . . 3  |-  ( A. x A. z ph  <->  A. z A. x ph )
32albii 1554 . 2  |-  ( A. y A. x A. z ph 
<-> 
A. y A. z A. x ph )
41, 3bitri 242 1  |-  ( A. x A. y A. z ph 
<-> 
A. y A. z A. x ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 178   A.wal 1532
This theorem is referenced by:  alrot4  1611  nfnid  4098  raliunxp  4732  dff13  5635
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-7 1535  ax-gen 1536
This theorem depends on definitions:  df-bi 179
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