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Theorem excomim 1758
Description: One direction of Theorem 19.11 of [Margaris] p. 89. Revised to remove dependency on ax-11 1762, ax-6 1745, ax-9 1667, ax-8 1688 and ax-17 1627. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Revised by Wolf Lammen, 8-Jan-2018.)
Assertion
Ref Expression
excomim  |-  ( E. x E. y ph  ->  E. y E. x ph )

Proof of Theorem excomim
StepHypRef Expression
1 excom 1757 . 2  |-  ( E. x E. y ph  <->  E. y E. x ph )
21biimpi 188 1  |-  ( E. x E. y ph  ->  E. y E. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1551
This theorem is referenced by:  excomOLD  1883  2euswap  2359  a9e2eq  28718  a9e2nd  28719  a9e2eqVD  29093  a9e2ndVD  29094  a9e2ndALT  29116
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-7 1750
This theorem depends on definitions:  df-bi 179  df-ex 1552
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