Description: The value of the Euclidean geometry for dimension N . (Contributed by Thierry Arnoux, 15-Mar-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | eengv | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq2 | |
|
2 | 1 | opeq2d | |
3 | 1 | adantr | |
4 | simpl | |
|
5 | 4 | oveq2d | |
6 | 5 | sumeq1d | |
7 | 1 3 6 | mpoeq123dva | |
8 | 7 | opeq2d | |
9 | 2 8 | preq12d | |
10 | 1 | adantr | |
11 | 10 | rabeqdv | |
12 | 1 3 11 | mpoeq123dva | |
13 | 12 | opeq2d | |
14 | 3 | difeq1d | |
15 | 1 | rabeqdv | |
16 | 15 | adantr | |
17 | 1 14 16 | mpoeq123dva | |
18 | 17 | opeq2d | |
19 | 13 18 | preq12d | |
20 | 9 19 | uneq12d | |
21 | df-eeng | |
|
22 | prex | |
|
23 | prex | |
|
24 | 22 23 | unex | |
25 | 20 21 24 | fvmpt | |