Theorem exrot4 1745

Description: Rotate existential quantifiers twice. (Contributed by NM, 9-Mar-1995.)

Assertion

Ref	Expression
exrot4	|- (E.xE.yE.zE.wph <-> E.zE.wE.xE.yph)

Proof of Theorem exrot4

Step	Hyp	Ref	Expression
1		excom13 1743	. . 3 |- (E.yE.zE.wph <-> E.wE.zE.yph)
2	1	exbii 1582	. 2 |- (E.xE.yE.zE.wph <-> E.xE.wE.zE.yph)
3		excom13 1743	. 2 |- (E.xE.wE.zE.yph <-> E.zE.wE.xE.yph)
4	2, 3	bitri 240	1 |- (E.xE.yE.zE.wph <-> E.zE.wE.xE.yph)

Syntax hints:   <-> wb 176  E.wex 1541

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  df-ex 1542

This theorem is referenced by:  sikexlem  4296  insklem  4305  elswap  4741  dfoprab2  5559  brpprod  5840  lecex  6116