Theorem pm2.61iii 159

Description: Inference eliminating three antecedents. (Contributed by NM, 2-Jan-2002.) (Proof shortened by Wolf Lammen, 22-Sep-2013.)

Hypotheses

Ref	Expression
pm2.61iii.1	⊢ (¬ φ → (¬ ψ → (¬ χ → θ)))
pm2.61iii.2	⊢ (φ → θ)
pm2.61iii.3	⊢ (ψ → θ)
pm2.61iii.4	⊢ (χ → θ)

Assertion

Ref	Expression
pm2.61iii	⊢ θ

Proof of Theorem pm2.61iii

Step	Hyp	Ref	Expression
1		pm2.61iii.4	. 2 ⊢ (χ → θ)
2		pm2.61iii.1	. . 3 ⊢ (¬ φ → (¬ ψ → (¬ χ → θ)))
3		pm2.61iii.2	. . . 4 ⊢ (φ → θ)
4	3	a1d 22	. . 3 ⊢ (φ → (¬ χ → θ))
5		pm2.61iii.3	. . . 4 ⊢ (ψ → θ)
6	5	a1d 22	. . 3 ⊢ (ψ → (¬ χ → θ))
7	2, 4, 6	pm2.61ii 157	. 2 ⊢ (¬ χ → θ)
8	1, 7	pm2.61i 156	1 ⊢ θ

Syntax hints:  ¬ wn 3   → wi 4

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

This theorem is referenced by: (None)