Theorem pm2.65i

Description: Inference for proof by contradiction. (Contributed by NM, 18-May-1994) (Proof shortened by Wolf Lammen, 11-Sep-2013) (Proof shortened by Garrett Katz, 7-Jun-2026)

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

Proof

Step	Hyp	Ref	Expression
1		pm2.65i.1	$$⊢\phi \to \psi$$
2		pm2.65i.2	$$⊢\phi \to \neg \psi$$
3	2 1	nsyl3	$$⊢\phi \to \neg \phi$$
4	3	pm2.01i	$$⊢\neg \phi$$