Description: The value of a linear combination. (Contributed by AV, 30-Mar-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | lincval | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lincop | |
|
2 | 1 | 3ad2ant1 | |
3 | 2 | oveqd | |
4 | simp2 | |
|
5 | simp3 | |
|
6 | ovexd | |
|
7 | simpr | |
|
8 | fveq1 | |
|
9 | 8 | oveq1d | |
10 | 9 | adantr | |
11 | 7 10 | mpteq12dv | |
12 | 11 | oveq2d | |
13 | oveq2 | |
|
14 | eqid | |
|
15 | 12 13 14 | ovmpox2 | |
16 | 4 5 6 15 | syl3anc | |
17 | 3 16 | eqtrd | |