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Theorem exrot4 1627
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 1625 . . 3  |-  ( E. y E. z E. w ph  <->  E. w E. z E. y ph )
21exbii 1542 . 2  |-  ( E. x E. y E. z E. w ph  <->  E. x E. w E. z E. y ph )
3 excom13 1625 . 2  |-  ( E. x E. w E. z E. y ph  <->  E. z E. w E. x E. y ph )
42, 3bitri 183 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 104   E.wex 1427
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-4 1446  ax-ial 1473
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  ee8anv  1859  elvvv  4516  dfoprab2  5712  xpassen  6602  enq0sym  7054
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