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Theorem exrot4 1761
Description: Rotate existential quantifiers twice. (Contributed by NM, 9-Mar-1995.)
Assertion
Ref Expression
exrot4  |-  ( E. x E. y E. z E. w ph  <->  E. z E. w E. x E. y ph )

Proof of Theorem exrot4
StepHypRef Expression
1 excom13 1759 . . 3  |-  ( E. y E. z E. w ph  <->  E. w E. z E. y ph )
21exbii 1593 . 2  |-  ( E. x E. y E. z E. w ph  <->  E. x E. w E. z E. y ph )
3 excom13 1759 . 2  |-  ( E. x E. w E. z E. y ph  <->  E. z E. w E. x E. y ph )
42, 3bitri 242 1  |-  ( E. x E. y E. z E. w ph  <->  E. z E. w E. x E. y ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 178   E.wex 1551
This theorem is referenced by:  elvvv  4939  dfoprab2  6123  xpassen  7204  5oalem7  23164  elfuns  25762
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-7 1750
This theorem depends on definitions:  df-bi 179  df-ex 1552
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