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Mirrors > Home > MPE Home > Th. List > df-fusgr | Structured version Visualization version GIF version |
Description: Define the class of all finite undirected simple graphs without loops (called "finite simple graphs" in the following). A finite simple graph is an undirected simple graph of finite order, i.e. with a finite set of vertices. (Contributed by AV, 3-Jan-2020.) (Revised by AV, 21-Oct-2020.) |
Ref | Expression |
---|---|
df-fusgr | ⊢ FinUSGraph = {𝑔 ∈ USGraph ∣ (Vtx‘𝑔) ∈ Fin} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cfusgr 26663 | . 2 class FinUSGraph | |
2 | vg | . . . . . 6 setvar 𝑔 | |
3 | 2 | cv 1600 | . . . . 5 class 𝑔 |
4 | cvtx 26344 | . . . . 5 class Vtx | |
5 | 3, 4 | cfv 6135 | . . . 4 class (Vtx‘𝑔) |
6 | cfn 8241 | . . . 4 class Fin | |
7 | 5, 6 | wcel 2106 | . . 3 wff (Vtx‘𝑔) ∈ Fin |
8 | cusgr 26498 | . . 3 class USGraph | |
9 | 7, 2, 8 | crab 3093 | . 2 class {𝑔 ∈ USGraph ∣ (Vtx‘𝑔) ∈ Fin} |
10 | 1, 9 | wceq 1601 | 1 wff FinUSGraph = {𝑔 ∈ USGraph ∣ (Vtx‘𝑔) ∈ Fin} |
Colors of variables: wff setvar class |
This definition is referenced by: isfusgr 26665 |
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