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Metamath Proof Explorer

Theorem con3i

Description: A contraposition inference. Inference associated with con3 . Its associated inference is mto . (Contributed by NM, 3-Jan-1993) (Proof shortened by Wolf Lammen, 20-Jun-2013)

		Ref	Expression
	Hypothesis	con3i.a	⊢ ( 𝜑 → 𝜓 )
	Assertion	con3i	⊢ ( ¬ 𝜓 → ¬ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		con3i.a	⊢ ( 𝜑 → 𝜓 )
2		id	⊢ ( ¬ 𝜓 → ¬ 𝜓 )
3	2 1	nsyl	⊢ ( ¬ 𝜓 → ¬ 𝜑 )