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Theorem excomim 1598
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 1527 . . 3  |-  ( ph  ->  E. x ph )
212eximi 1537 . 2  |-  ( E. x E. y ph  ->  E. x E. y E. x ph )
3 hbe1 1429 . . . 4  |-  ( E. x ph  ->  A. x E. x ph )
43hbex 1572 . . 3  |-  ( E. y E. x ph  ->  A. x E. y E. x ph )
5419.9h 1579 . 2  |-  ( E. x E. y E. x ph  <->  E. y E. x ph )
62, 5sylib 120 1  |-  ( E. x E. y ph  ->  E. y E. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1426
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-ial 1472
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  excom  1599  2euswapdc  2039
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