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Theorem excomim 1753
Description: One direction of Theorem 19.11 of [Margaris] p. 89. Revised to remove dependency on ax-11 1757, ax-6 1740, ax-9 1662, ax-8 1683 and ax-17 1623. (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 1752 . 2  |-  ( E. x E. y ph  <->  E. y E. x ph )
21biimpi 187 1  |-  ( E. x E. y ph  ->  E. y E. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1547
This theorem is referenced by:  excomOLD  1878  2euswap  2330  a9e2eq  28355  a9e2nd  28356  a9e2eqVD  28728  a9e2ndVD  28729  a9e2ndALT  28752
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-7 1745
This theorem depends on definitions:  df-bi 178  df-ex 1548
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