Theorem excomim 2199

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 1942, ax-6 1999, ax-7 2040, ax-10 2177, ax-12 2212. (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 2198	. 2 ⊢ (∃𝑥∃𝑦𝜑 ↔ ∃𝑦∃𝑥𝜑)
2	1	biimpi 219	1 ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑)

This proof depends on syntax axioms:   → wi 4  ∃wex 1811

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-11 2193

This proof depends on definitions:  df-bi 210  df-ex 1812

This theorem is used by:  nfexhe  2210  2euswapv  2655  2euswap  2670  relopabi  5799  lfuhgr3  29733  umgr2cycl  30752  bj-cbveximd  37623  ax6e2eq  45633  ax6e2nd  45634  ax6e2eqVD  45982  ax6e2ndVD  45983  ax6e2ndALT  46005