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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	$⊢ \neg φ \to ψ$
	Assertion	con1i	$⊢ \neg ψ \to φ$

Proof

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