Theorem con3i

Description: A contraposition inference. Inference associated with con3 . Its associated inference is mto . (Contributed by NM, 3-Jan-1993) (Proof shortened by Wolf Lammen, 20-Jun-2013)

	Ref	Expression
Hypothesis	con3i.a	$$⊢\phi \to \psi$$
Assertion	con3i	$$⊢\neg \psi \to \neg \phi$$

Proof

Step	Hyp	Ref	Expression
1		con3i.a	$$⊢\phi \to \psi$$
2		id	$$⊢\neg \psi \to \neg \psi$$
3	2 1	nsyl	$$⊢\neg \psi \to \neg \phi$$