Theorem excomim 2163

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 1910, ax-6 1967, ax-7 2007, ax-10 2141, ax-12 2177. (Revised by Wolf Lammen, 8-Jan-2018.)

Assertion

Ref	Expression
excomim	⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑)

Proof of Theorem excomim

Step	Hyp	Ref	Expression
1		excom 2162	. 2 ⊢ (∃𝑥∃𝑦𝜑 ↔ ∃𝑦∃𝑥𝜑)
2	1	biimpi 216	1 ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑)

Syntax hints:   → wi 4  ∃wex 1779

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-11 2157

This theorem depends on definitions:  df-bi 207  df-ex 1780

This theorem is referenced by:  2euswapv  2630  2euswap  2645  relopabi  5832  lfuhgr3  35125  umgr2cycl  35146  ax6e2eq  44577  ax6e2nd  44578  ax6e2eqVD  44927  ax6e2ndVD  44928  ax6e2ndALT  44950