Theorem alrot4 1095

Description: Rotate 4 universal quantifiers twice.

Assertion

Ref	Expression
alrot4	|- (A.xA.yA.zA.wph <-> A.zA.wA.xA.yph)

Proof of Theorem alrot4

Step	Hyp	Ref	Expression
1		alcom 1030	. . . 4 |- (A.yA.zA.wph <-> A.zA.yA.wph)
2		alcom 1030	. . . . 5 |- (A.yA.wph <-> A.wA.yph)
3	2	albii 997	. . . 4 |- (A.zA.yA.wph <-> A.zA.wA.yph)
4	1, 3	bitr 173	. . 3 |- (A.yA.zA.wph <-> A.zA.wA.yph)
5	4	albii 997	. 2 |- (A.xA.yA.zA.wph <-> A.xA.zA.wA.yph)
6		alcom 1030	. 2 |- (A.xA.zA.wA.yph <-> A.zA.xA.wA.yph)
7		alcom 1030	. . 3 |- (A.xA.wA.yph <-> A.wA.xA.yph)
8	7	albii 997	. 2 |- (A.zA.xA.wA.yph <-> A.zA.wA.xA.yph)
9	5, 6, 8	3bitr 177	1 |- (A.xA.yA.zA.wph <-> A.zA.wA.xA.yph)

Syntax hints:   <-> wb 146  A.wal 952

This theorem is referenced by:  2mo 1445  fun11 3554

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-4 971  ax-5o 973

This theorem depends on definitions:  df-bi 147  df-an 225

Copyright terms: Public domain