Theorem orcnd

Description: A lemma for Conjunctive Normal Form unit propagation, in deduction form. (Contributed by Giovanni Mascellani, 15-Sep-2017)

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

Proof

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