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Theorem excom13 1758
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 1756 . 2  |-  ( E. x E. y E. z ph  <->  E. y E. x E. z ph )
2 excom 1756 . . 3  |-  ( E. x E. z ph  <->  E. z E. x ph )
32exbii 1592 . 2  |-  ( E. y E. x E. z ph  <->  E. y E. z E. x ph )
4 excom 1756 . 2  |-  ( E. y E. z E. x ph  <->  E. z E. y E. x ph )
51, 3, 43bitri 263 1  |-  ( E. x E. y E. z ph  <->  E. z E. y E. x ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 177   E.wex 1550
This theorem is referenced by:  exrot3  1759  exrot4  1760  euotd  4449
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-7 1749
This theorem depends on definitions:  df-bi 178  df-ex 1551
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