Theorem mt3i 118

Description: Modus tollens inference. (Contributed by NM, 26-Mar-1995.) (Proof shortened by Wolf Lammen, 15-Sep-2012.)

Hypotheses

Ref	Expression
mt3i.1	⊢ ¬ χ
mt3i.2	⊢ (φ → (¬ ψ → χ))

Assertion

Ref	Expression
mt3i	⊢ (φ → ψ)

Proof of Theorem mt3i

Step	Hyp	Ref	Expression
1		mt3i.1	. . 3 ⊢ ¬ χ
2	1	a1i 10	. 2 ⊢ (φ → ¬ χ)
3		mt3i.2	. 2 ⊢ (φ → (¬ ψ → χ))
4	2, 3	mt3d 117	1 ⊢ (φ → ψ)

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)