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Mirrors > Home > MPE Home > Th. List > df-rusgr | Structured version Visualization version GIF version |
Description: Define the "k-regular simple graph" predicate, which is true for a simple graph being k-regular: read 𝐺 RegUSGraph 𝐾 as 𝐺 is a 𝐾-regular simple graph. (Contributed by Alexander van der Vekens, 6-Jul-2018.) (Revised by AV, 18-Dec-2020.) |
Ref | Expression |
---|---|
df-rusgr | ⊢ RegUSGraph = {⟨𝑔, 𝑘⟩ ∣ (𝑔 ∈ USGraph ∧ 𝑔 RegGraph 𝑘)} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | crusgr 28810 | . 2 class RegUSGraph | |
2 | vg | . . . . . 6 setvar 𝑔 | |
3 | 2 | cv 1540 | . . . . 5 class 𝑔 |
4 | cusgr 28406 | . . . . 5 class USGraph | |
5 | 3, 4 | wcel 2106 | . . . 4 wff 𝑔 ∈ USGraph |
6 | vk | . . . . . 6 setvar 𝑘 | |
7 | 6 | cv 1540 | . . . . 5 class 𝑘 |
8 | crgr 28809 | . . . . 5 class RegGraph | |
9 | 3, 7, 8 | wbr 5148 | . . . 4 wff 𝑔 RegGraph 𝑘 |
10 | 5, 9 | wa 396 | . . 3 wff (𝑔 ∈ USGraph ∧ 𝑔 RegGraph 𝑘) |
11 | 10, 2, 6 | copab 5210 | . 2 class {⟨𝑔, 𝑘⟩ ∣ (𝑔 ∈ USGraph ∧ 𝑔 RegGraph 𝑘)} |
12 | 1, 11 | wceq 1541 | 1 wff RegUSGraph = {⟨𝑔, 𝑘⟩ ∣ (𝑔 ∈ USGraph ∧ 𝑔 RegGraph 𝑘)} |
Colors of variables: wff setvar class |
This definition is referenced by: isrusgr 28815 rusgrprop 28816 |
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