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Theorem excomim 2083
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 1879, ax-6 1945, ax-7 1981, ax-10 2059, ax-12 2087. (Revised by Wolf Lammen, 8-Jan-2018.)
Assertion
Ref Expression
excomim (∃𝑥𝑦𝜑 → ∃𝑦𝑥𝜑)

Proof of Theorem excomim
StepHypRef Expression
1 excom 2082 . 2 (∃𝑥𝑦𝜑 ↔ ∃𝑦𝑥𝜑)
21biimpi 206 1 (∃𝑥𝑦𝜑 → ∃𝑦𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1744
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-11 2074
This theorem depends on definitions:  df-bi 197  df-ex 1745
This theorem is referenced by:  2euswap  2577  relopabi  5278  ax6e2eq  39090  ax6e2nd  39091  ax6e2eqVD  39457  ax6e2ndVD  39458  ax6e2ndALT  39480
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