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Metamath Proof Explorer

Theorem con1

Description: Contraposition. Theorem *2.15 of WhiteheadRussell p. 102. Its associated inference is con1i . (Contributed by NM, 29-Dec-1992) (Proof shortened by Wolf Lammen, 12-Feb-2013)

		Ref	Expression
	Assertion	con1	$⊢ (\neg φ \to ψ) \to (\neg ψ \to φ)$

Proof

Step	Hyp	Ref	Expression
1		id	$⊢ (\neg φ \to ψ) \to (\neg φ \to ψ)$
2	1	con1d	$⊢ (\neg φ \to ψ) \to (\neg ψ \to φ)$