Theorem sumeq2d

Description: Equality deduction for sum. Note that unlike sumeq2dv , k may occur in ph . (Contributed by NM, 1-Nov-2005)

	Ref	Expression
Hypothesis	sumeq2d.1	|- ( ph -> A. k e. A B = C )
Assertion	sumeq2d	|- ( ph -> sum_ k e. A B = sum_ k e. A C )

Proof

Step	Hyp	Ref	Expression
1		sumeq2d.1	|- ( ph -> A. k e. A B = C )
2		sumeq2	|- ( A. k e. A B = C -> sum_ k e. A B = sum_ k e. A C )
3	1 2	syl	|- ( ph -> sum_ k e. A B = sum_ k e. A C )