Theorem ord

Description: Deduce implication from disjunction. (Contributed by NM, 18-May-1994)

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

Proof

Step	Hyp	Ref	Expression
1		ord.1	$$⊢\phi \to \left(\psi \vee \chi \right)$$
2		df-or	$$⊢\left(\psi \vee \chi \right)\leftrightarrow \left(\neg \psi \to \chi \right)$$
3	1 2	sylib	$$⊢\phi \to \left(\neg \psi \to \chi \right)$$