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Theorem exrot3 1818
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 1817 . 2  |-  ( E. x E. y E. z ph  <->  E. z E. y E. x ph )
2 excom 1786 . 2  |-  ( E. z E. y E. x ph  <->  E. y E. z E. x ph )
31, 2bitri 240 1  |-  ( E. x E. y E. z ph  <->  E. y E. z E. x ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 176   E.wex 1528
This theorem is referenced by:  opabn0  4295  dmoprab  5928  rnoprab  5930  xpassen  6956  brimg  24476  ellines  24775
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-tru 1310  df-ex 1529  df-nf 1532
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