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Metamath Proof Explorer

Theorem mt2bi

Description: A false consequent falsifies an antecedent. (Contributed by NM, 19-Aug-1993) (Proof shortened by Wolf Lammen, 12-Nov-2012)

		Ref	Expression
	Hypothesis	mt2bi.1	$⊢ φ$
	Assertion	mt2bi	$⊢ \neg ψ \leftrightarrow (ψ \to \neg φ)$

Step	Hyp	Ref	Expression
1		mt2bi.1	$⊢ φ$
2	1	a1bi	$⊢ \neg ψ \leftrightarrow (φ \to \neg ψ)$
3		con2b	$⊢ (φ \to \neg ψ) \leftrightarrow (ψ \to \neg φ)$
4	2 3	bitri	$⊢ \neg ψ \leftrightarrow (ψ \to \neg φ)$