Description: Equality inference for sum. (Contributed by FL, 10-Dec-2006)
Ref | Expression | ||
---|---|---|---|
Hypotheses | sumeq12i.1 | |- A = B |
|
sumeq12i.2 | |- ( k e. A -> C = D ) |
||
Assertion | sumeq12i | |- sum_ k e. A C = sum_ k e. B D |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sumeq12i.1 | |- A = B |
|
2 | sumeq12i.2 | |- ( k e. A -> C = D ) |
|
3 | 2 | sumeq2i | |- sum_ k e. A C = sum_ k e. A D |
4 | 1 | sumeq1i | |- sum_ k e. A D = sum_ k e. B D |
5 | 3 4 | eqtri | |- sum_ k e. A C = sum_ k e. B D |