Theorem jaoi

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

	Ref	Expression
Hypotheses	jaoi.1	$$⊢\phi \to \psi$$
	jaoi.2	$$⊢\chi \to \psi$$
Assertion	jaoi	$$⊢\left(\phi \vee \chi \right)\to \psi$$

Proof

Step	Hyp	Ref	Expression
1		jaoi.1	$$⊢\phi \to \psi$$
2		jaoi.2	$$⊢\chi \to \psi$$
3		pm2.53	$$⊢\left(\phi \vee \chi \right)\to \left(\neg \phi \to \chi \right)$$
4	3 2	syl6	$$⊢\left(\phi \vee \chi \right)\to \left(\neg \phi \to \psi \right)$$
5	4 1	pm2.61d2	$$⊢\left(\phi \vee \chi \right)\to \psi$$