Theorem pm2.65da

Description: Deduction for proof by contradiction. (Contributed by NM, 12-Jun-2014)

	Ref	Expression
Hypotheses	pm2.65da.1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
	pm2.65da.2	$$⊢\left(\phi \wedge \psi \right)\to \neg \chi$$
Assertion	pm2.65da	$$⊢\phi \to \neg \psi$$

Proof

Step	Hyp	Ref	Expression
1		pm2.65da.1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
2		pm2.65da.2	$$⊢\left(\phi \wedge \psi \right)\to \neg \chi$$
3	1	ex	$$⊢\phi \to \left(\psi \to \chi \right)$$
4	2	ex	$$⊢\phi \to \left(\psi \to \neg \chi \right)$$
5	3 4	pm2.65d	$$⊢\phi \to \neg \psi$$