Theorem orrd

Description: Deduce disjunction from implication. (Contributed by NM, 27-Nov-1995)

	Ref	Expression
Hypothesis	orrd.1	$$⊢\phi \to \left(\neg \psi \to \chi \right)$$
Assertion	orrd	$$⊢\phi \to \left(\psi \vee \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		orrd.1	$$⊢\phi \to \left(\neg \psi \to \chi \right)$$
2		pm2.54	$$⊢\left(\neg \psi \to \chi \right)\to \left(\psi \vee \chi \right)$$
3	1 2	syl	$$⊢\phi \to \left(\psi \vee \chi \right)$$