Theorem sumeq2i

Description: Equality inference for sum. (Contributed by NM, 3-Dec-2005)

	Ref	Expression
Hypothesis	sumeq2i.1	$$⊢k\in A\to B=C$$
Assertion	sumeq2i	$$⊢\sum _{k\in A}B=\sum _{k\in A}C$$

Proof

Step	Hyp	Ref	Expression
1		sumeq2i.1	$$⊢k\in A\to B=C$$
2		sumeq2	$$⊢\forall k\in AB=C\to \sum _{k\in A}B=\sum _{k\in A}C$$
3	2 1	mprg	$$⊢\sum _{k\in A}B=\sum _{k\in A}C$$