Metamath Proof Explorer


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 φ ¬ ψ
Assertion con2i ψ ¬ φ

Proof

Step Hyp Ref Expression
1 con2i.a φ ¬ ψ
2 id ψ ψ
3 1 2 nsyl3 ψ ¬ φ