Theorem excomim 2198

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 1940, ax-6 1997, ax-7 2038, ax-10 2176, ax-12 2213. (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 2197	. 2 ⊢ (∃𝑥∃𝑦𝜑 ↔ ∃𝑦∃𝑥𝜑)
2	1	biimpi 219	1 ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑)

Syntax hints:   → wi 4  ∃wex 1809

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-11 2192

This theorem depends on definitions:  df-bi 210  df-ex 1810

This theorem is referenced by:  nfexhe  2211  2euswapv  2658  2euswap  2673  relopabi  5811  lfuhgr3  35590  umgr2cycl  35611  bj-cbveximd  37232  ax6e2eq  45246  ax6e2nd  45247  ax6e2eqVD  45595  ax6e2ndVD  45596  ax6e2ndALT  45618