Theorem sumeq2sdv

Description: Equality deduction for sum. (Contributed by NM, 3-Jan-2006) (Proof shortened by Glauco Siliprandi, 5-Apr-2020)

	Ref	Expression
Hypothesis	sumeq2sdv.1	$$⊢\phi \to B=C$$
Assertion	sumeq2sdv	$$⊢\phi \to \sum _{k\in A}B=\sum _{k\in A}C$$

Proof

Step	Hyp	Ref	Expression
1		sumeq2sdv.1	$$⊢\phi \to B=C$$
2	1	ralrimivw	$$⊢\phi \to \forall k\in AB=C$$
3	2	sumeq2d	$$⊢\phi \to \sum _{k\in A}B=\sum _{k\in A}C$$