Theorem alrot3 1414

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

Step	Hyp	Ref	Expression
1		alcom 1407	. 2 |- ( A. x A. y A. z ph <-> A. y A. x A. z ph )
2		alcom 1407	. . 3 |- ( A. x A. z ph <-> A. z A. x ph )
3	2	albii 1399	. 2 |- ( A. y A. x A. z ph <-> A. y A. z A. x ph )
4	1, 3	bitri 182	1 |- ( A. x A. y A. z ph <-> A. y A. z A. x ph )

Syntax hints:   <-> wb 103   A.wal 1282

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 1376  ax-7 1377  ax-gen 1378

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  alrot4  1415  raliunxp  4495  dff13  5428