Theorem excomim 2174

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 1917, ax-6 1974, ax-7 2015, ax-10 2152, ax-12 2189. (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 2173	. 2 ⊢ (∃𝑥∃𝑦𝜑 ↔ ∃𝑦∃𝑥𝜑)
2	1	biimpi 217	1 ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑)

Syntax hints:   → wi 4  ∃wex 1786

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-11 2168

This theorem depends on definitions:  df-bi 208  df-ex 1787

This theorem is referenced by:  nfexhe  2187  2euswapv  2634  2euswap  2649  relopabi  5772  lfuhgr3  35355  umgr2cycl  35376  bj-cbveximd  36979  ax6e2eq  45008  ax6e2nd  45009  ax6e2eqVD  45357  ax6e2ndVD  45358  ax6e2ndALT  45380