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	⊢ ( 𝜑 → 𝜓 )
	pm2.61i.2	⊢ ( ¬ 𝜑 → 𝜓 )
Assertion	pm2.61i	⊢ 𝜓

Proof

Step	Hyp	Ref	Expression
1		pm2.61i.1	⊢ ( 𝜑 → 𝜓 )
2		pm2.61i.2	⊢ ( ¬ 𝜑 → 𝜓 )
3	1 2	nsyl4	⊢ ( ¬ 𝜓 → 𝜓 )
4	3	pm2.18i	⊢ 𝜓