Theorem excomim 2196

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 1929, ax-6 1986, ax-7 2027, ax-10 2174, ax-12 2211. (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 2195	. 2 ⊢ (∃𝑥∃𝑦𝜑 ↔ ∃𝑦∃𝑥𝜑)
2	1	biimpi 218	1 ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑)

Syntax hints:   → wi 4  ∃wex 1798

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-11 2190

This theorem depends on definitions:  df-bi 209  df-ex 1799

This theorem is referenced by:  nfexhe  2209  2euswapv  2656  2euswap  2671  relopabi  5793  lfuhgr3  35434  umgr2cycl  35455  bj-cbveximd  37068  ax6e2eq  45097  ax6e2nd  45098  ax6e2eqVD  45446  ax6e2ndVD  45447  ax6e2ndALT  45469