Theorem sumeq1i

Description: Equality inference for sum. (Contributed by NM, 2-Jan-2006)

	Ref	Expression
Hypothesis	sumeq1i.1	$$⊢A=B$$
Assertion	sumeq1i	$$⊢\sum _{k\in A}C=\sum _{k\in B}C$$

Proof

Step	Hyp	Ref	Expression
1		sumeq1i.1	$$⊢A=B$$
2		sumeq1	$$⊢A=B\to \sum _{k\in A}C=\sum _{k\in B}C$$
3	1 2	ax-mp	$$⊢\sum _{k\in A}C=\sum _{k\in B}C$$