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 )