Theorem nsyld 132

Description: A negated syllogism deduction. (Contributed by NM, 9-Apr-2005.)

Hypotheses

Ref	Expression
nsyld.1	⊢ (φ → (ψ → ¬ χ))
nsyld.2	⊢ (φ → (τ → χ))

Assertion

Ref	Expression
nsyld	⊢ (φ → (ψ → ¬ τ))

Proof of Theorem nsyld

Step	Hyp	Ref	Expression
1		nsyld.1	. 2 ⊢ (φ → (ψ → ¬ χ))
2		nsyld.2	. . 3 ⊢ (φ → (τ → χ))
3	2	con3d 125	. 2 ⊢ (φ → (¬ χ → ¬ τ))
4	1, 3	syld 40	1 ⊢ (φ → (ψ → ¬ τ))

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:  pm2.65d  166  sbn  2062  enprmaplem3  6079  nnc3n3p1  6279