Theorem alrot3 2038

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 2037	. 2 |- ( A. x A. y A. z ph <-> A. y A. x A. z ph )
2		alcom 2037	. . 3 |- ( A. x A. z ph <-> A. z A. x ph )
3	2	albii 1747	. 2 |- ( A. y A. x A. z ph <-> A. y A. z A. x ph )
4	1, 3	bitri 264	1 |- ( A. x A. y A. z ph <-> A. y A. z A. x ph )

Syntax hints:   <-> wb 196   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-11 2034

This theorem depends on definitions:  df-bi 197

This theorem is referenced by:  alrot4  2039  nfnid  4897  raliunxp  5261  dff13  6512  undmrnresiss  37910  ntrneikb  38392  ntrneixb  38393