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Metamath Proof Explorer

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	⊢ ( ¬ 𝜑 → 𝜓 )
	Assertion	con1i	⊢ ( ¬ 𝜓 → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		con1i.1	⊢ ( ¬ 𝜑 → 𝜓 )
2		id	⊢ ( ¬ 𝜓 → ¬ 𝜓 )
3	2 1	nsyl2	⊢ ( ¬ 𝜓 → 𝜑 )