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Theorem exrot4 1858
Description: Rotate existential quantifiers twice. (Contributed by NM, 9-Mar-1995.)
Assertion
Ref Expression
exrot4  |-  ( E. x E. y E. z E. w ph  <->  E. z E. w E. x E. y ph )

Proof of Theorem exrot4
StepHypRef Expression
1 excom13 1856 . . 3  |-  ( E. y E. z E. w ph  <->  E. w E. z E. y ph )
21exbii 1672 . 2  |-  ( E. x E. y E. z E. w ph  <->  E. x E. w E. z E. y ph )
3 excom13 1856 . 2  |-  ( E. x E. w E. z E. y ph  <->  E. z E. w E. x E. y ph )
42, 3bitri 249 1  |-  ( E. x E. y E. z E. w ph  <->  E. z E. w E. x E. y ph )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184   E.wex 1617
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-11 1847
This theorem depends on definitions:  df-bi 185  df-ex 1618
This theorem is referenced by:  elvvv  5048  dfoprab2  6316  xpassen  7604  5oalem7  26776  elfuns  29793
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