MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  excomim Structured version   Visualization version   GIF version

Theorem excomim 2029
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 1826, ax-6 1874, ax-7 1921, ax-10 2005, ax-12 2033. (Revised by Wolf Lammen, 8-Jan-2018.)
Assertion
Ref Expression
excomim (∃𝑥𝑦𝜑 → ∃𝑦𝑥𝜑)

Proof of Theorem excomim
StepHypRef Expression
1 excom 2028 . 2 (∃𝑥𝑦𝜑 ↔ ∃𝑦𝑥𝜑)
21biimpi 204 1 (∃𝑥𝑦𝜑 → ∃𝑦𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1694
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-11 2020
This theorem depends on definitions:  df-bi 195  df-ex 1695
This theorem is referenced by:  2euswap  2535  ax6e2eq  37618  ax6e2nd  37619  ax6e2eqVD  37989  ax6e2ndVD  37990  ax6e2ndALT  38012
  Copyright terms: Public domain W3C validator