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Theorem excom13 1859
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 1857 . 2  |-  ( E. x E. y E. z ph  <->  E. y E. x E. z ph )
2 excom 1857 . . 3  |-  ( E. x E. z ph  <->  E. z E. x ph )
32exbii 1675 . 2  |-  ( E. y E. x E. z ph  <->  E. y E. z E. x ph )
4 excom 1857 . 2  |-  ( E. y E. z E. x ph  <->  E. z E. y E. x ph )
51, 3, 43bitri 271 1  |-  ( E. x E. y E. z ph  <->  E. z E. y E. x ph )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184   E.wex 1620
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1626  ax-4 1639  ax-11 1850
This theorem depends on definitions:  df-bi 185  df-ex 1621
This theorem is referenced by:  exrot3  1860  exrot4  1861  euotd  4662  elfuns  29718
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