Theorem pm2.65ni

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

	Ref	Expression
Hypotheses	pm2.65ni.1	⊢ ( ¬ 𝜑 → 𝜓 )
	pm2.65ni.2	⊢ ( ¬ 𝜑 → ¬ 𝜓 )
Assertion	pm2.65ni	⊢ 𝜑

Proof

Step	Hyp	Ref	Expression
1		pm2.65ni.1	⊢ ( ¬ 𝜑 → 𝜓 )
2		pm2.65ni.2	⊢ ( ¬ 𝜑 → ¬ 𝜓 )
3	1 2	pm2.65i	⊢ ¬ ¬ 𝜑
4	3	notnotri	⊢ 𝜑