Theorem sumeq1d

Description: Equality deduction for sum. (Contributed by NM, 1-Nov-2005)

	Ref	Expression
Hypothesis	sumeq1d.1	$$⊢\phi \to A=B$$
Assertion	sumeq1d	$$⊢\phi \to \sum _{k\in A}C=\sum _{k\in B}C$$

Proof

Step	Hyp	Ref	Expression
1		sumeq1d.1	$$⊢\phi \to A=B$$
2		sumeq1	$$⊢A=B\to \sum _{k\in A}C=\sum _{k\in B}C$$
3	1 2	syl	$$⊢\phi \to \sum _{k\in A}C=\sum _{k\in B}C$$