Theorem alrot3 1485

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 1478	. 2 |- ( A. x A. y A. z ph <-> A. y A. x A. z ph )
2		alcom 1478	. . 3 |- ( A. x A. z ph <-> A. z A. x ph )
3	2	albii 1470	. 2 |- ( A. y A. x A. z ph <-> A. y A. z A. x ph )
4	1, 3	bitri 184	1 |- ( A. x A. y A. z ph <-> A. y A. z A. x ph )

Syntax hints:   <-> wb 105   A.wal 1351

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  alrot4  1486  raliunxp  4770  dff13  5771