Theorem sumeq2i

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

	Ref	Expression
Hypothesis	sumeq2i.1	|- ( k e. A -> B = C )
Assertion	sumeq2i	|- sum_ k e. A B = sum_ k e. A C

Proof

Step	Hyp	Ref	Expression
1		sumeq2i.1	|- ( k e. A -> B = C )
2		sumeq2	|- ( A. k e. A B = C -> sum_ k e. A B = sum_ k e. A C )
3	2 1	mprg	|- sum_ k e. A B = sum_ k e. A C