Theorem alrot4 1739

Description: Rotate 4 universal quantifiers twice. (Contributed by NM, 2-Feb-2005.) (Proof shortened by Fan Zheng, 6-Jun-2016.)

Assertion

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

Proof of Theorem alrot4

Step	Hyp	Ref	Expression
1		alrot3 1738	. . 3 |- (A.yA.zA.wph <-> A.zA.wA.yph)
2	1	albii 1566	. 2 |- (A.xA.yA.zA.wph <-> A.xA.zA.wA.yph)
3		alrot3 1738	. 2 |- (A.xA.zA.wA.yph <-> A.zA.wA.xA.yph)
4	2, 3	bitri 240	1 |- (A.xA.yA.zA.wph <-> A.zA.wA.xA.yph)

Syntax hints:   <-> wb 176  A.wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-7 1734

This theorem depends on definitions:  df-bi 177

This theorem is referenced by:  2mo  2282  fun11  5160