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Metamath Proof Explorer

Theorem con2

Description: Contraposition. Theorem *2.03 of WhiteheadRussell p. 100. (Contributed by NM, 29-Dec-1992) (Proof shortened by Wolf Lammen, 12-Feb-2013)

		Ref	Expression
	Assertion	con2	$⊢ (φ \to \neg ψ) \to (ψ \to \neg φ)$

Proof

Step	Hyp	Ref	Expression
1		id	$⊢ (φ \to \neg ψ) \to (φ \to \neg ψ)$
2	1	con2d	$⊢ (φ \to \neg ψ) \to (ψ \to \neg φ)$