Theorem con1i

Description: A contraposition inference. Inference associated with con1 . Its associated inference is mt3 . (Contributed by NM, 3-Jan-1993) (Proof shortened by Mel L. O'Cat, 28-Nov-2008) (Proof shortened by Wolf Lammen, 19-Jun-2013)

	Ref	Expression
Hypothesis	con1i.1	$$⊢\neg \phi \to \psi$$
Assertion	con1i	$$⊢\neg \psi \to \phi$$

Proof

Step	Hyp	Ref	Expression
1		con1i.1	$$⊢\neg \phi \to \psi$$
2		id	$$⊢\neg \psi \to \neg \psi$$
3	2 1	nsyl2	$$⊢\neg \psi \to \phi$$