Theorem nf3or

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

	Ref	Expression
Hypotheses	nf.1	$$⊢Ⅎx\phi$$
	nf.2	$$⊢Ⅎx\psi$$
	nf.3	$$⊢Ⅎx\chi$$
Assertion	nf3or	$$⊢Ⅎx\left(\phi \vee \psi \vee \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		nf.1	$$⊢Ⅎx\phi$$
2		nf.2	$$⊢Ⅎx\psi$$
3		nf.3	$$⊢Ⅎx\chi$$
4		df-3or	$$⊢\left(\phi \vee \psi \vee \chi \right)\leftrightarrow \left(\left(\phi \vee \psi \right)\vee \chi \right)$$
5	1 2	nfor	$$⊢Ⅎx\left(\phi \vee \psi \right)$$
6	5 3	nfor	$$⊢Ⅎx\left(\left(\phi \vee \psi \right)\vee \chi \right)$$
7	4 6	nfxfr	$$⊢Ⅎx\left(\phi \vee \psi \vee \chi \right)$$