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Theorem exrot3 1701
Description: Rotate existential quantifiers. (Contributed by NM, 17-Mar-1995.)
Assertion
Ref Expression
exrot3  |-  ( E. x E. y E. z ph  <->  E. y E. z E. x ph )

Proof of Theorem exrot3
StepHypRef Expression
1 excom13 1700 . 2  |-  ( E. x E. y E. z ph  <->  E. z E. y E. x ph )
2 excom 1675 . 2  |-  ( E. z E. y E. x ph  <->  E. y E. z E. x ph )
31, 2bitri 184 1  |-  ( E. x E. y E. z ph  <->  E. y E. z E. x ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 105   E.wex 1503
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-ial 1545
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  opabm  4298  rexiunxp  4787  dmoprab  5977  rnoprab  5979  cnvoprab  6259  xpassen  6856  dmaddpq  7408  dmmulpq  7409
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