Theorem pm2.18da

Description: Deduction based on reductio ad absurdum. See pm2.18 . (Contributed by Mario Carneiro, 9-Feb-2017)

	Ref	Expression
Hypothesis	pm2.18da.1	$$⊢\left(\phi \wedge \neg \psi \right)\to \psi$$
Assertion	pm2.18da	$$⊢\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		pm2.18da.1	$$⊢\left(\phi \wedge \neg \psi \right)\to \psi$$
2	1	ex	$$⊢\phi \to \left(\neg \psi \to \psi \right)$$
3	2	pm2.18d	$$⊢\phi \to \psi$$