Theorem con2i

Description: A contraposition inference. Its associated inference is mt2 . (Contributed by NM, 10-Jan-1993) (Proof shortened by Mel L. O'Cat, 28-Nov-2008) (Proof shortened by Wolf Lammen, 13-Jun-2013)

	Ref	Expression
Hypothesis	con2i.a	$$⊢\phi \to \neg \psi$$
Assertion	con2i	$$⊢\psi \to \neg \phi$$

Proof

Step	Hyp	Ref	Expression
1		con2i.a	$$⊢\phi \to \neg \psi$$
2		id	$$⊢\psi \to \psi$$
3	1 2	nsyl3	$$⊢\psi \to \neg \phi$$