Theorem jaoi3

Description: Inference separating a disjunct of an antecedent. (Contributed by Alexander van der Vekens, 25-May-2018)

	Ref	Expression
Hypotheses	jaoi3.1	$$⊢\phi \to \psi$$
	jaoi3.2	$$⊢\left(\neg \phi \wedge \chi \right)\to \psi$$
Assertion	jaoi3	$$⊢\left(\phi \vee \chi \right)\to \psi$$

Proof

Step	Hyp	Ref	Expression
1		jaoi3.1	$$⊢\phi \to \psi$$
2		jaoi3.2	$$⊢\left(\neg \phi \wedge \chi \right)\to \psi$$
3	1 2	jaoi	$$⊢\left(\phi \vee \left(\neg \phi \wedge \chi \right)\right)\to \psi$$
4	3	jaoi2	$$⊢\left(\phi \vee \chi \right)\to \psi$$