Theorem excomim 2161

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 1908, ax-6 1965, ax-7 2005, ax-10 2139, ax-12 2175. (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 2160	. 2 ⊢ (∃𝑥∃𝑦𝜑 ↔ ∃𝑦∃𝑥𝜑)
2	1	biimpi 216	1 ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑)

Syntax hints:   → wi 4  ∃wex 1776

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-11 2155

This theorem depends on definitions:  df-bi 207  df-ex 1777

This theorem is referenced by:  2euswapv  2628  2euswap  2643  relopabi  5835  lfuhgr3  35104  umgr2cycl  35126  ax6e2eq  44555  ax6e2nd  44556  ax6e2eqVD  44905  ax6e2ndVD  44906  ax6e2ndALT  44928