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Theorem exrot3 1792
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 1791 . 2  |-  ( E. x E. y E. z ph  <->  E. z E. y E. x ph )
2 excom 1789 . 2  |-  ( E. z E. y E. x ph  <->  E. y E. z E. x ph )
31, 2bitri 249 1  |-  ( E. x E. y E. z ph  <->  E. y E. z E. x ph )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184   E.wex 1587
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-11 1782
This theorem depends on definitions:  df-bi 185  df-ex 1588
This theorem is referenced by:  opabn0  4730  dmoprab  6284  rnoprab  6286  xpassen  7518  elima4  27757  brimg  28135  ellines  28350
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