Theorem excomim 2200

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 1943, ax-6 2000, ax-7 2041, ax-10 2178, 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 2199	. 2 ⊢ (∃𝑥∃𝑦𝜑 ↔ ∃𝑦∃𝑥𝜑)
2	1	biimpi 219	1 ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑)

This proof depends on syntax axioms:   → wi 4  ∃wex 1812

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-11 2194

This proof depends on definitions:  df-bi 210  df-ex 1813

This theorem is used by:  nfexhe  2211  2euswapv  2656  2euswap  2671  relopabi  5800  lfuhgr3  29710  umgr2cycl  30729  bj-cbveximd  37501  ax6e2eq  45499  ax6e2nd  45500  ax6e2eqVD  45848  ax6e2ndVD  45849  ax6e2ndALT  45871