Theorem pm2.65ni

Description: Inference rule for proof by contradiction. (Contributed by Glauco Siliprandi, 5-Apr-2020)

	Ref	Expression
Hypotheses	pm2.65ni.1	$$⊢\neg \phi \to \psi$$
	pm2.65ni.2	$$⊢\neg \phi \to \neg \psi$$
Assertion	pm2.65ni	$$⊢\phi$$

Proof

Step	Hyp	Ref	Expression
1		pm2.65ni.1	$$⊢\neg \phi \to \psi$$
2		pm2.65ni.2	$$⊢\neg \phi \to \neg \psi$$
3	1 2	pm2.65i	$$⊢\neg \neg \phi$$
4	3	notnotri	$$⊢\phi$$