Theorem nfanOLD 1826

Description: Obsolete proof of nfan 1824 as of 2-Jan-2018. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nfan.1	⊢ Ⅎxφ
nfan.2	⊢ Ⅎxψ

Assertion

Ref	Expression
nfanOLD	⊢ Ⅎx(φ ∧ ψ)

Proof of Theorem nfanOLD

Step	Hyp	Ref	Expression
1		df-an 360	. 2 ⊢ ((φ ∧ ψ) ↔ ¬ (φ → ¬ ψ))
2		nfan.1	. . . 4 ⊢ Ⅎxφ
3		nfan.2	. . . . 5 ⊢ Ⅎxψ
4	3	nfn 1793	. . . 4 ⊢ Ⅎx ¬ ψ
5	2, 4	nfim 1813	. . 3 ⊢ Ⅎx(φ → ¬ ψ)
6	5	nfn 1793	. 2 ⊢ Ⅎx ¬ (φ → ¬ ψ)
7	1, 6	nfxfr 1570	1 ⊢ Ⅎx(φ ∧ ψ)

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 358  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-11 1746

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545

This theorem is referenced by: (None)