Theorem excomim 2156

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 1906, ax-6 1964, ax-7 2004, ax-10 2130, ax-12 2164. (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 2155	. 2 ⊢ (∃𝑥∃𝑦𝜑 ↔ ∃𝑦∃𝑥𝜑)
2	1	biimpi 215	1 ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑)

Syntax hints:   → wi 4  ∃wex 1774

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-11 2147

This theorem depends on definitions:  df-bi 206  df-ex 1775

This theorem is referenced by:  2euswapv  2621  2euswap  2636  relopabi  5818  lfuhgr3  34665  umgr2cycl  34687  ax6e2eq  43919  ax6e2nd  43920  ax6e2eqVD  44269  ax6e2ndVD  44270  ax6e2ndALT  44292