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Theorem excomim 2164
Description: One direction of Theorem 19.11 of [Margaris] p. 89. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) Remove dependencies on ax-5 1914, ax-6 1972, ax-7 2012, ax-10 2138, ax-12 2172. (Revised by Wolf Lammen, 8-Jan-2018.)
Assertion
Ref Expression
excomim (∃𝑥𝑦𝜑 → ∃𝑦𝑥𝜑)

Proof of Theorem excomim
StepHypRef Expression
1 excom 2163 . 2 (∃𝑥𝑦𝜑 ↔ ∃𝑦𝑥𝜑)
21biimpi 215 1 (∃𝑥𝑦𝜑 → ∃𝑦𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1782
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-11 2155
This theorem depends on definitions:  df-bi 206  df-ex 1783
This theorem is referenced by:  2euswapv  2627  2euswap  2642  relopabi  5823  lfuhgr3  34110  umgr2cycl  34132  ax6e2eq  43318  ax6e2nd  43319  ax6e2eqVD  43668  ax6e2ndVD  43669  ax6e2ndALT  43691
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