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Theorem excom13 1829
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 1798 . 2  |-  ( E. x E. y E. z ph  <->  E. y E. x E. z ph )
2 excom 1798 . . 3  |-  ( E. x E. z ph  <->  E. z E. x ph )
32exbii 1572 . 2  |-  ( E. y E. x E. z ph  <->  E. y E. z E. x ph )
4 excom 1798 . 2  |-  ( E. y E. z E. x ph  <->  E. z E. y E. x ph )
51, 3, 43bitri 262 1  |-  ( E. x E. y E. z ph  <->  E. z E. y E. x ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 176   E.wex 1531
This theorem is referenced by:  exrot3  1830  exrot4  1831  euotd  4283
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-tru 1310  df-ex 1532  df-nf 1535
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