Theorem exrot4 778

Description: Rotate existential quantifiers twice.

Assertion

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

Proof of Theorem exrot4

Step	Hyp	Ref	Expression
1		excom13 776	. . 3 |- (E.yE.zE.wph <-> E.wE.zE.yph)
2	1	biex 733	. 2 |- (E.xE.yE.zE.wph <-> E.xE.wE.zE.yph)
3		excom13 776	. 2 |- (E.xE.wE.zE.yph <-> E.zE.wE.xE.yph)
4	2, 3	bitr 151	1 |- (E.xE.yE.zE.wph <-> E.zE.wE.xE.yph)

Syntax hints:   <-> wb 127  E.wex 678

This theorem is referenced by:  dfoprab2 3021  xpassen 3344  genpass 3906  distrlem1pr 3921  distrlem5pr 3925  5oalem7 5550

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

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