Theorem nsyl2 119

Description: A negated syllogism inference. (Contributed by NM, 26-Jun-1994.)

Hypotheses

Ref	Expression
nsyl2.1	⊢ (φ → ¬ ψ)
nsyl2.2	⊢ (¬ χ → ψ)

Assertion

Ref	Expression
nsyl2	⊢ (φ → χ)

Proof of Theorem nsyl2

Step	Hyp	Ref	Expression
1		nsyl2.1	. 2 ⊢ (φ → ¬ ψ)
2		nsyl2.2	. . 3 ⊢ (¬ χ → ψ)
3	2	a1i 10	. 2 ⊢ (φ → (¬ χ → ψ))
4	1, 3	mt3d 117	1 ⊢ (φ → χ)

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:  con1i  121  con4i  122  dvelimv  1939  ecexr  5950