Theorem notornotel2

Description: A lemma for not-or-not elimination, in deduction form. (Contributed by Giovanni Mascellani, 19-Mar-2018)

	Ref	Expression
Hypothesis	notornotel2.1	$$⊢\phi \to \neg \left(\psi \vee \neg \chi \right)$$
Assertion	notornotel2	$$⊢\phi \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		notornotel2.1	$$⊢\phi \to \neg \left(\psi \vee \neg \chi \right)$$
2		orcom	$$⊢\left(\neg \chi \vee \psi \right)\leftrightarrow \left(\psi \vee \neg \chi \right)$$
3	1 2	sylnibr	$$⊢\phi \to \neg \left(\neg \chi \vee \psi \right)$$
4	3	notornotel1	$$⊢\phi \to \chi$$