Theorem excomimOLD 1858

Description: Obsolete proof of excomim 1742 as of 8-Jan-2018. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem excomimOLD

Step	Hyp	Ref	Expression
1		19.8a 1756	. . 3 ⊢ (φ → ∃xφ)
2	1	2eximi 1577	. 2 ⊢ (∃x∃yφ → ∃x∃y∃xφ)
3		nfe1 1732	. . . 4 ⊢ Ⅎx∃xφ
4	3	nfex 1843	. . 3 ⊢ Ⅎx∃y∃xφ
5	4	19.9 1783	. 2 ⊢ (∃x∃y∃xφ ↔ ∃y∃xφ)
6	2, 5	sylib 188	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-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545

This theorem is referenced by: (None)