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Theorem exrot4 1691
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 1689 . . 3  |-  ( E. y E. z E. w ph  <->  E. w E. z E. y ph )
21exbii 1605 . 2  |-  ( E. x E. y E. z E. w ph  <->  E. x E. w E. z E. y ph )
3 excom13 1689 . 2  |-  ( E. x E. w E. z E. y ph  <->  E. z E. w E. x E. y ph )
42, 3bitri 184 1  |-  ( E. x E. y E. z E. w ph  <->  E. z E. w E. x E. y ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 105   E.wex 1492
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  ee8anv  1935  elvvv  4691  dfoprab2  5924  xpassen  6832  enq0sym  7433
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