Theorem excomim 2162

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 1912, ax-6 1970, ax-7 2010, ax-10 2136, ax-12 2170. (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 2161	. 2 ⊢ (∃𝑥∃𝑦𝜑 ↔ ∃𝑦∃𝑥𝜑)
2	1	biimpi 215	1 ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑)

Syntax hints:   → wi 4  ∃wex 1780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-11 2153

This theorem depends on definitions:  df-bi 206  df-ex 1781

This theorem is referenced by:  2euswapv  2631  2euswap  2646  relopabi  5752  lfuhgr3  33220  umgr2cycl  33242  ax6e2eq  42411  ax6e2nd  42412  ax6e2eqVD  42761  ax6e2ndVD  42762  ax6e2ndALT  42784