Theorem condan

Description: Proof by contradiction. (Contributed by NM, 9-Feb-2006) (Proof shortened by Wolf Lammen, 19-Jun-2014)

	Ref	Expression
Hypotheses	condan.1	$$⊢\left(\phi \wedge \neg \psi \right)\to \chi$$
	condan.2	$$⊢\left(\phi \wedge \neg \psi \right)\to \neg \chi$$
Assertion	condan	$$⊢\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		condan.1	$$⊢\left(\phi \wedge \neg \psi \right)\to \chi$$
2		condan.2	$$⊢\left(\phi \wedge \neg \psi \right)\to \neg \chi$$
3	1 2	pm2.65da	$$⊢\phi \to \neg \neg \psi$$
4	3	notnotrd	$$⊢\phi \to \psi$$