Theorem excomim 1742

Description: One direction of Theorem 19.11 of [Margaris] p. 89. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Revised by Wolf Lammen to remove dependency on ax-11 1746 ax-6 1729 ax-9 1654 ax-8 1675 and ax-17 1616, 8-Jan-2018.)

Assertion

Ref	Expression
excomim	⊢ (∃x∃yφ → ∃y∃xφ)

Proof of Theorem excomim

Step	Hyp	Ref	Expression
1		excom 1741	. 2 ⊢ (∃x∃yφ ↔ ∃y∃xφ)
2	1	biimpi 186	1 ⊢ (∃x∃yφ → ∃y∃xφ)

Syntax hints:   → wi 4  ∃wex 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-7 1734

This theorem depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by:  excomOLD  1859  2euswap  2280