Theorem alrot4 2039

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

Assertion

Ref	Expression
alrot4	|- ( A. x A. y A. z A. w ph <-> A. z A. w A. x A. y ph )

Proof of Theorem alrot4

Step	Hyp	Ref	Expression
1		alrot3 2038	. . 3 |- ( A. y A. z A. w ph <-> A. z A. w A. y ph )
2	1	albii 1747	. 2 |- ( A. x A. y A. z A. w ph <-> A. x A. z A. w A. y ph )
3		alrot3 2038	. 2 |- ( A. x A. z A. w A. y ph <-> A. z A. w A. x A. y ph )
4	2, 3	bitri 264	1 |- ( A. x A. y A. z A. w ph <-> A. z A. w A. x A. y 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:  2mo  2551  fun11  5963