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Theorem excomim 1764
Description: One direction of Theorem 19.11 of [Margaris] p. 89. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.)
Assertion
Ref Expression
excomim  |-  ( E. x E. y ph  ->  E. y E. x ph )

Proof of Theorem excomim
StepHypRef Expression
1 19.8a 1758 . . 3  |-  ( ph  ->  E. x ph )
212eximi 1575 . 2  |-  ( E. x E. y ph  ->  E. x E. y E. x ph )
3 nfe1 1566 . . . 4  |-  F/ x E. x ph
43nfex 1733 . . 3  |-  F/ x E. y E. x ph
5419.9 1762 . 2  |-  ( E. x E. y E. x ph  <->  E. y E. x ph )
62, 5sylib 190 1  |-  ( E. x E. y ph  ->  E. y E. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 6   E.wex 1537
This theorem is referenced by:  excom  1765  2euswap  2189  a9e2eq  27016  a9e2nd  27017  a9e2eqVD  27373  a9e2ndVD  27374  a9e2ndALT  27397
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-tru 1315  df-ex 1538  df-nf 1540
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