Theorem nfexOLD 1844

Description: Obsolete proof of nfex 1843 as of 30-Dec-2017. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
nfal.1	⊢ Ⅎxφ

Assertion

Ref	Expression
nfexOLD	⊢ Ⅎx∃yφ

Proof of Theorem nfexOLD

Step	Hyp	Ref	Expression
1		df-ex 1542	. 2 ⊢ (∃yφ ↔ ¬ ∀y ¬ φ)
2		nfal.1	. . . . 5 ⊢ Ⅎxφ
3	2	nfn 1793	. . . 4 ⊢ Ⅎx ¬ φ
4	3	nfal 1842	. . 3 ⊢ Ⅎx∀y ¬ φ
5	4	nfn 1793	. 2 ⊢ Ⅎx ¬ ∀y ¬ φ
6	1, 5	nfxfr 1570	1 ⊢ Ⅎx∃yφ

Syntax hints:  ¬ wn 3  ∀wal 1540  ∃wex 1541  Ⅎwnf 1544

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-tru 1319  df-ex 1542  df-nf 1545

This theorem is referenced by: (None)