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Theorem exrot4 1831
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 1829 . . 3  |-  ( E. y E. z E. w ph  <->  E. w E. z E. y ph )
21exbii 1572 . 2  |-  ( E. x E. y E. z E. w ph  <->  E. x E. w E. z E. y ph )
3 excom13 1829 . 2  |-  ( E. x E. w E. z E. y ph  <->  E. z E. w E. x E. y ph )
42, 3bitri 240 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 176   E.wex 1531
This theorem is referenced by:  elvvv  4765  dfoprab2  5911  xpassen  6972  5oalem7  22255
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-tru 1310  df-ex 1532  df-nf 1535
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