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Metamath Proof Explorer
Definition df-ub
Description: Define the upper bound relationship functor. See brub for value.
(Contributed by Scott Fenton, 3-May-2018)
|
|
Ref |
Expression |
|
Assertion |
df-ub |
⊢ UB 𝑅 = ( ( V × V ) ∖ ( ( V ∖ 𝑅 ) ∘ ◡ E ) ) |
Detailed syntax breakdown
| Step |
Hyp |
Ref |
Expression |
| 0 |
|
cR |
⊢ 𝑅 |
| 1 |
0
|
cub |
⊢ UB 𝑅 |
| 2 |
|
cvv |
⊢ V |
| 3 |
2 2
|
cxp |
⊢ ( V × V ) |
| 4 |
2 0
|
cdif |
⊢ ( V ∖ 𝑅 ) |
| 5 |
|
cep |
⊢ E |
| 6 |
5
|
ccnv |
⊢ ◡ E |
| 7 |
4 6
|
ccom |
⊢ ( ( V ∖ 𝑅 ) ∘ ◡ E ) |
| 8 |
3 7
|
cdif |
⊢ ( ( V × V ) ∖ ( ( V ∖ 𝑅 ) ∘ ◡ E ) ) |
| 9 |
1 8
|
wceq |
⊢ UB 𝑅 = ( ( V × V ) ∖ ( ( V ∖ 𝑅 ) ∘ ◡ E ) ) |