Theorem olcnd

Description: A lemma for Conjunctive Normal Form unit propagation, in deduction form. (Contributed by Giovanni Mascellani, 15-Sep-2017) (Proof shortened by Wolf Lammen, 13-Apr-2024)

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

Proof

Step	Hyp	Ref	Expression
1		olcnd.1	$$⊢\phi \to \left(\psi \vee \chi \right)$$
2		olcnd.2	$$⊢\phi \to \neg \chi$$
3	1	ord	$$⊢\phi \to \left(\neg \psi \to \chi \right)$$
4	2 3	mt3d	$$⊢\phi \to \psi$$