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Metamath Proof Explorer

Theorem con3ALT2

Description: Contraposition. Alternate proof of con3 . This proof is con3ALTVD automatically translated and minimized. (Contributed by Alan Sare, 21-Apr-2013) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	con3ALT2	⊢ ( ( 𝜑 → 𝜓 ) → ( ¬ 𝜓 → ¬ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		notnotr	⊢ ( ¬ ¬ 𝜑 → 𝜑 )
2	1	imim1i	⊢ ( ( 𝜑 → 𝜓 ) → ( ¬ ¬ 𝜑 → 𝜓 ) )
3	2	con1d	⊢ ( ( 𝜑 → 𝜓 ) → ( ¬ 𝜓 → ¬ 𝜑 ) )