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Theorem exrot3 1596
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 1595 . 2  |-  ( E. x E. y E. z ph  <->  E. z E. y E. x ph )
2 excom 1570 . 2  |-  ( E. z E. y E. x ph  <->  E. y E. z E. x ph )
31, 2bitri 177 1  |-  ( E. x E. y E. z ph  <->  E. y E. z E. x ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 102   E.wex 1397
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-ial 1443
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  opabm  4045  rexiunxp  4506  dmoprab  5613  rnoprab  5615  cnvoprab  5883  xpassen  6335  dmaddpq  6535  dmmulpq  6536
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