Theorem excomim 2169

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 1969, ax-7 2010, ax-10 2147, ax-12 2185. (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 2168	. 2 ⊢ (∃𝑥∃𝑦𝜑 ↔ ∃𝑦∃𝑥𝜑)
2	1	biimpi 216	1 ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑)

Syntax hints:   → wi 4  ∃wex 1781

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-11 2163

This theorem depends on definitions:  df-bi 207  df-ex 1782

This theorem is referenced by:  nfexhe  2183  2euswapv  2631  2euswap  2646  relopabi  5779  lfuhgr3  35333  umgr2cycl  35354  ax6e2eq  44907  ax6e2nd  44908  ax6e2eqVD  45256  ax6e2ndVD  45257  ax6e2ndALT  45279