Step |
Hyp |
Ref |
Expression |
0 |
|
cuvc |
⊢ unitVec |
1 |
|
vr |
⊢ 𝑟 |
2 |
|
cvv |
⊢ V |
3 |
|
vi |
⊢ 𝑖 |
4 |
|
vj |
⊢ 𝑗 |
5 |
3
|
cv |
⊢ 𝑖 |
6 |
|
vk |
⊢ 𝑘 |
7 |
6
|
cv |
⊢ 𝑘 |
8 |
4
|
cv |
⊢ 𝑗 |
9 |
7 8
|
wceq |
⊢ 𝑘 = 𝑗 |
10 |
|
cur |
⊢ 1r |
11 |
1
|
cv |
⊢ 𝑟 |
12 |
11 10
|
cfv |
⊢ ( 1r ‘ 𝑟 ) |
13 |
|
c0g |
⊢ 0g |
14 |
11 13
|
cfv |
⊢ ( 0g ‘ 𝑟 ) |
15 |
9 12 14
|
cif |
⊢ if ( 𝑘 = 𝑗 , ( 1r ‘ 𝑟 ) , ( 0g ‘ 𝑟 ) ) |
16 |
6 5 15
|
cmpt |
⊢ ( 𝑘 ∈ 𝑖 ↦ if ( 𝑘 = 𝑗 , ( 1r ‘ 𝑟 ) , ( 0g ‘ 𝑟 ) ) ) |
17 |
4 5 16
|
cmpt |
⊢ ( 𝑗 ∈ 𝑖 ↦ ( 𝑘 ∈ 𝑖 ↦ if ( 𝑘 = 𝑗 , ( 1r ‘ 𝑟 ) , ( 0g ‘ 𝑟 ) ) ) ) |
18 |
1 3 2 2 17
|
cmpo |
⊢ ( 𝑟 ∈ V , 𝑖 ∈ V ↦ ( 𝑗 ∈ 𝑖 ↦ ( 𝑘 ∈ 𝑖 ↦ if ( 𝑘 = 𝑗 , ( 1r ‘ 𝑟 ) , ( 0g ‘ 𝑟 ) ) ) ) ) |
19 |
0 18
|
wceq |
⊢ unitVec = ( 𝑟 ∈ V , 𝑖 ∈ V ↦ ( 𝑗 ∈ 𝑖 ↦ ( 𝑘 ∈ 𝑖 ↦ if ( 𝑘 = 𝑗 , ( 1r ‘ 𝑟 ) , ( 0g ‘ 𝑟 ) ) ) ) ) |