Theorem jaoi

Description: Inference disjoining the antecedents of two implications. (Contributed by NM, 5-Apr-1994)

	Ref	Expression
Hypotheses	jaoi.1	⊢ ( 𝜑 → 𝜓 )
	jaoi.2	⊢ ( 𝜒 → 𝜓 )
Assertion	jaoi	⊢ ( ( 𝜑 ∨ 𝜒 ) → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		jaoi.1	⊢ ( 𝜑 → 𝜓 )
2		jaoi.2	⊢ ( 𝜒 → 𝜓 )
3		pm2.53	⊢ ( ( 𝜑 ∨ 𝜒 ) → ( ¬ 𝜑 → 𝜒 ) )
4	3 2	syl6	⊢ ( ( 𝜑 ∨ 𝜒 ) → ( ¬ 𝜑 → 𝜓 ) )
5	4 1	pm2.61d2	⊢ ( ( 𝜑 ∨ 𝜒 ) → 𝜓 )