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Theorem excomim 2170
 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 1911, ax-6 1970, ax-7 2015, ax-10 2145, ax-12 2178. (Revised by Wolf Lammen, 8-Jan-2018.)
Assertion
Ref Expression
excomim (∃𝑥𝑦𝜑 → ∃𝑦𝑥𝜑)

Proof of Theorem excomim
StepHypRef Expression
1 excom 2169 . 2 (∃𝑥𝑦𝜑 ↔ ∃𝑦𝑥𝜑)
21biimpi 219 1 (∃𝑥𝑦𝜑 → ∃𝑦𝑥𝜑)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∃wex 1781 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-11 2161 This theorem depends on definitions:  df-bi 210  df-ex 1782 This theorem is referenced by:  2euswapv  2716  2euswap  2731  relopabi  5671  lfuhgr3  32440  umgr2cycl  32462  ax6e2eq  41197  ax6e2nd  41198  ax6e2eqVD  41547  ax6e2ndVD  41548  ax6e2ndALT  41570
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