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	⊢ Ⅎ 𝑥 𝜑
	nf.2	⊢ Ⅎ 𝑥 𝜓
	nf.3	⊢ Ⅎ 𝑥 𝜒
Assertion	nf3or	⊢ Ⅎ 𝑥 ( 𝜑 ∨ 𝜓 ∨ 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		nf.1	⊢ Ⅎ 𝑥 𝜑
2		nf.2	⊢ Ⅎ 𝑥 𝜓
3		nf.3	⊢ Ⅎ 𝑥 𝜒
4		df-3or	⊢ ( ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) ↔ ( ( 𝜑 ∨ 𝜓 ) ∨ 𝜒 ) )
5	1 2	nfor	⊢ Ⅎ 𝑥 ( 𝜑 ∨ 𝜓 )
6	5 3	nfor	⊢ Ⅎ 𝑥 ( ( 𝜑 ∨ 𝜓 ) ∨ 𝜒 )
7	4 6	nfxfr	⊢ Ⅎ 𝑥 ( 𝜑 ∨ 𝜓 ∨ 𝜒 )