Theorem mt4i 131

Description: Modus tollens inference. (Contributed by Wolf Lammen, 12-May-2013.)

Hypotheses

Ref	Expression
mt4i.1	⊢ χ
mt4i.2	⊢ (φ → (¬ ψ → ¬ χ))

Assertion

Ref	Expression
mt4i	⊢ (φ → ψ)

Proof of Theorem mt4i

Step	Hyp	Ref	Expression
1		mt4i.1	. . 3 ⊢ χ
2	1	a1i 10	. 2 ⊢ (φ → χ)
3		mt4i.2	. 2 ⊢ (φ → (¬ ψ → ¬ χ))
4	2, 3	mt4d 130	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)