Theorem exrot4 1102

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 1100	. . 3 |- (E.yE.zE.wph <-> E.wE.zE.yph)
2	1	exbii 1053	. 2 |- (E.xE.yE.zE.wph <-> E.xE.wE.zE.yph)
3		excom13 1100	. 2 |- (E.xE.wE.zE.yph <-> E.zE.wE.xE.yph)
4	2, 3	bitr 173	1 |- (E.xE.yE.zE.wph <-> E.zE.wE.xE.yph)

Syntax hints:   <-> wb 146  E.wex 982

This theorem is referenced by:  dfoprab2 3997  xpassen 4447  genpass 5124  distrlem1pr 5139  distrlem5pr 5143  5oalem7 9600

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-4 975  ax-5o 977  ax-6o 980

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983

Copyright terms: Public domain