Theorem pm2.61i

Description: Inference eliminating an antecedent. (Contributed by NM, 5-Apr-1994) (Proof shortened by Wolf Lammen, 19-Nov-2023)

	Ref	Expression
Hypotheses	pm2.61i.1	$$⊢\phi \to \psi$$
	pm2.61i.2	$$⊢\neg \phi \to \psi$$
Assertion	pm2.61i	$$⊢\psi$$

Proof

Step	Hyp	Ref	Expression
1		pm2.61i.1	$$⊢\phi \to \psi$$
2		pm2.61i.2	$$⊢\neg \phi \to \psi$$
3	1 2	nsyl4	$$⊢\neg \psi \to \psi$$
4	3	pm2.18i	$$⊢\psi$$