Theorem csbeq1d

Description: Equality deduction for proper substitution into a class. (Contributed by NM, 3-Dec-2005)

	Ref	Expression
Hypothesis	csbeq1d.1	$$⊢\phi \to A=B$$
Assertion	csbeq1d	$$⊢\phi \to ⦋A/x⦌C=⦋B/x⦌C$$

Proof

Step	Hyp	Ref	Expression
1		csbeq1d.1	$$⊢\phi \to A=B$$
2		csbeq1	$$⊢A=B\to ⦋A/x⦌C=⦋B/x⦌C$$
3	1 2	syl	$$⊢\phi \to ⦋A/x⦌C=⦋B/x⦌C$$