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Metamath Proof Explorer

Theorem con5

Description: Biconditional contraposition variation. This proof is con5VD automatically translated and minimized. (Contributed by Alan Sare, 21-Apr-2013) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	con5	⊢ ( ( 𝜑 ↔ ¬ 𝜓 ) → ( ¬ 𝜑 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		biimpr	⊢ ( ( 𝜑 ↔ ¬ 𝜓 ) → ( ¬ 𝜓 → 𝜑 ) )
2	1	con1d	⊢ ( ( 𝜑 ↔ ¬ 𝜓 ) → ( ¬ 𝜑 → 𝜓 ) )