Theorem nfor

Description: If x is not free in ph and ps , then it is not free in ( ph \/ ps ) . (Contributed by NM, 5-Aug-1993) (Revised by Mario Carneiro, 11-Aug-2016)

	Ref	Expression
Hypotheses	nf.1	$$⊢Ⅎx\phi$$
	nf.2	$$⊢Ⅎx\psi$$
Assertion	nfor	$$⊢Ⅎx\left(\phi \vee \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		nf.1	$$⊢Ⅎx\phi$$
2		nf.2	$$⊢Ⅎx\psi$$
3		df-or	$$⊢\left(\phi \vee \psi \right)\leftrightarrow \left(\neg \phi \to \psi \right)$$
4	1	nfn	$$⊢Ⅎx\neg \phi$$
5	4 2	nfim	$$⊢Ⅎx\left(\neg \phi \to \psi \right)$$
6	3 5	nfxfr	$$⊢Ⅎx\left(\phi \vee \psi \right)$$