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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-ub | Structured version Visualization version GIF version |
Description: Define the upper bound relationship functor. See brub 33993 for value. (Contributed by Scott Fenton, 3-May-2018.) |
Ref | Expression |
---|---|
df-ub | ⊢ UB𝑅 = ((V × V) ∖ ((V ∖ 𝑅) ∘ ◡ E )) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cR | . . 3 class 𝑅 | |
2 | 1 | cub 33891 | . 2 class UB𝑅 |
3 | cvv 3408 | . . . 4 class V | |
4 | 3, 3 | cxp 5549 | . . 3 class (V × V) |
5 | 3, 1 | cdif 3863 | . . . 4 class (V ∖ 𝑅) |
6 | cep 5459 | . . . . 5 class E | |
7 | 6 | ccnv 5550 | . . . 4 class ◡ E |
8 | 5, 7 | ccom 5555 | . . 3 class ((V ∖ 𝑅) ∘ ◡ E ) |
9 | 4, 8 | cdif 3863 | . 2 class ((V × V) ∖ ((V ∖ 𝑅) ∘ ◡ E )) |
10 | 2, 9 | wceq 1543 | 1 wff UB𝑅 = ((V × V) ∖ ((V ∖ 𝑅) ∘ ◡ E )) |
Colors of variables: wff setvar class |
This definition is referenced by: brub 33993 |
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