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Theorem excomim 1787
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 1720 . . 3  |-  ( ph  ->  E. x ph )
212eximi 1564 . 2  |-  ( E. x E. y ph  ->  E. x E. y E. x ph )
3 nfe1 1707 . . . 4  |-  F/ x E. x ph
43nfex 1769 . . 3  |-  F/ x E. y E. x ph
5419.9 1785 . 2  |-  ( E. x E. y E. x ph  <->  E. y E. x ph )
62, 5sylib 188 1  |-  ( E. x E. y ph  ->  E. y E. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1528
This theorem is referenced by:  excom  1788  2euswap  2220  a9e2eq  27606  a9e2nd  27607  a9e2eqVD  27963  a9e2ndVD  27964  a9e2ndALT  27987
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1636  ax-8 1644  ax-6 1704  ax-7 1709  ax-11 1716
This theorem depends on definitions:  df-bi 177  df-tru 1310  df-ex 1529  df-nf 1532
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