Theorem csbied

Description: Conversion of implicit substitution to explicit substitution into a class. (Contributed by Mario Carneiro, 2-Dec-2014) (Revised by Mario Carneiro, 13-Oct-2016)

	Ref	Expression
Hypotheses	csbied.1	$$⊢\phi \to A\in V$$
	csbied.2	$$⊢\left(\phi \wedge x=A\right)\to B=C$$
Assertion	csbied	$$⊢\phi \to ⦋A/x⦌B=C$$

Proof

Step	Hyp	Ref	Expression
1		csbied.1	$$⊢\phi \to A\in V$$
2		csbied.2	$$⊢\left(\phi \wedge x=A\right)\to B=C$$
3		nfv	$$⊢Ⅎx\phi$$
4		nfcvd	$$⊢\phi \to \underset{\_}{Ⅎ}xC$$
5	3 4 1 2	csbiedf	$$⊢\phi \to ⦋A/x⦌B=C$$