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Theorem excom13 1667
Description: Swap 1st and 3rd existential quantifiers. (Contributed by NM, 9-Mar-1995.)
Assertion
Ref Expression
excom13  |-  ( E. x E. y E. z ph  <->  E. z E. y E. x ph )

Proof of Theorem excom13
StepHypRef Expression
1 excom 1642 . 2  |-  ( E. x E. y E. z ph  <->  E. y E. x E. z ph )
2 excom 1642 . . 3  |-  ( E. x E. z ph  <->  E. z E. x ph )
32exbii 1584 . 2  |-  ( E. y E. x E. z ph  <->  E. y E. z E. x ph )
4 excom 1642 . 2  |-  ( E. y E. z E. x ph  <->  E. z E. y E. x ph )
51, 3, 43bitri 205 1  |-  ( E. x E. y E. z ph  <->  E. z E. y E. x ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 104   E.wex 1468
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-ial 1514
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  exrot3  1668  exrot4  1669  euotd  4171
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