Theorem nfss

Description: If x is not free in A and B , it is not free in A C_ B . (Contributed by NM, 27-Dec-1996)

	Ref	Expression
Hypotheses	dfssf.1	$$⊢\underset{\_}{Ⅎ}xA$$
	dfssf.2	$$⊢\underset{\_}{Ⅎ}xB$$
Assertion	nfss	$$⊢ℲxA\subseteq B$$

Proof

Step	Hyp	Ref	Expression
1		dfssf.1	$$⊢\underset{\_}{Ⅎ}xA$$
2		dfssf.2	$$⊢\underset{\_}{Ⅎ}xB$$
3	1 2	dfss3f	$$⊢A\subseteq B\leftrightarrow \forall x\in Ax\in B$$
4		nfra1	$$⊢Ⅎx\forall x\in Ax\in B$$
5	3 4	nfxfr	$$⊢ℲxA\subseteq B$$