Theorem excomim 2152

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 1905, ax-6 1963, ax-7 2003, ax-10 2129, ax-12 2166. (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 2151	. 2 ⊢ (∃𝑥∃𝑦𝜑 ↔ ∃𝑦∃𝑥𝜑)
2	1	biimpi 215	1 ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑)

Syntax hints:   → wi 4  ∃wex 1773

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-11 2146

This theorem depends on definitions:  df-bi 206  df-ex 1774

This theorem is referenced by:  2euswapv  2618  2euswap  2633  relopabi  5823  lfuhgr3  34799  umgr2cycl  34821  ax6e2eq  44061  ax6e2nd  44062  ax6e2eqVD  44411  ax6e2ndVD  44412  ax6e2ndALT  44434