Theorem csbied2

Description: Conversion of implicit substitution to explicit class substitution, deduction form. (Contributed by Mario Carneiro, 2-Jan-2017)

	Ref	Expression
Hypotheses	csbied2.1	$$⊢\phi \to A\in V$$
	csbied2.2	$$⊢\phi \to A=B$$
	csbied2.3	$$⊢\left(\phi \wedge x=B\right)\to C=D$$
Assertion	csbied2	$$⊢\phi \to ⦋A/x⦌C=D$$

Proof

Step	Hyp	Ref	Expression
1		csbied2.1	$$⊢\phi \to A\in V$$
2		csbied2.2	$$⊢\phi \to A=B$$
3		csbied2.3	$$⊢\left(\phi \wedge x=B\right)\to C=D$$
4		id	$$⊢x=A\to x=A$$
5	4 2	sylan9eqr	$$⊢\left(\phi \wedge x=A\right)\to x=B$$
6	5 3	syldan	$$⊢\left(\phi \wedge x=A\right)\to C=D$$
7	1 6	csbied	$$⊢\phi \to ⦋A/x⦌C=D$$