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Theorem excomim 1663
Description: One direction of Theorem 19.11 of [Margaris] p. 89. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
excomim  |-  ( E. x E. y ph  ->  E. y E. x ph )

Proof of Theorem excomim
StepHypRef Expression
1 19.8a 1590 . . 3  |-  ( ph  ->  E. x ph )
212eximi 1601 . 2  |-  ( E. x E. y ph  ->  E. x E. y E. x ph )
3 hbe1 1495 . . . 4  |-  ( E. x ph  ->  A. x E. x ph )
43hbex 1636 . . 3  |-  ( E. y E. x ph  ->  A. x E. y E. x ph )
5419.9h 1643 . 2  |-  ( E. x E. y E. x ph  <->  E. y E. x ph )
62, 5sylib 122 1  |-  ( E. x E. y ph  ->  E. y E. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   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:  excom  1664  2euswapdc  2117
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