Theorem csbconstgf

Description: Substitution doesn't affect a constant B (in which x is not free). (Contributed by NM, 10-Nov-2005)

	Ref	Expression
Hypothesis	csbconstgf.1	$$⊢\underset{\_}{Ⅎ}xB$$
Assertion	csbconstgf	$$⊢A\in V\to ⦋A/x⦌B=B$$

Proof

Step	Hyp	Ref	Expression
1		csbconstgf.1	$$⊢\underset{\_}{Ⅎ}xB$$
2		csbtt	$$⊢\left(A\in V\wedge \underset{\_}{Ⅎ}xB\right)\to ⦋A/x⦌B=B$$
3	1 2	mpan2	$$⊢A\in V\to ⦋A/x⦌B=B$$