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Definition df-vtx 26486
Description: Define the function mapping a graph to the set of its vertices. This definition is very general: It defines the set of vertices for any ordered pair as its first component, and for any other class as its "base set". It is meaningful, however, only if the ordered pair represents a graph resp. the class is an extensible structure representing a graph. (Contributed by AV, 9-Jan-2020.) (Revised by AV, 20-Sep-2020.)
Assertion
Ref Expression
df-vtx Vtx = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (1st𝑔), (Base‘𝑔)))

Detailed syntax breakdown of Definition df-vtx
StepHypRef Expression
1 cvtx 26484 . 2 class Vtx
2 vg . . 3 setvar 𝑔
3 cvv 3415 . . 3 class V
42cv 1506 . . . . 5 class 𝑔
53, 3cxp 5405 . . . . 5 class (V × V)
64, 5wcel 2050 . . . 4 wff 𝑔 ∈ (V × V)
7 c1st 7499 . . . . 5 class 1st
84, 7cfv 6188 . . . 4 class (1st𝑔)
9 cbs 16339 . . . . 5 class Base
104, 9cfv 6188 . . . 4 class (Base‘𝑔)
116, 8, 10cif 4350 . . 3 class if(𝑔 ∈ (V × V), (1st𝑔), (Base‘𝑔))
122, 3, 11cmpt 5008 . 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (1st𝑔), (Base‘𝑔)))
131, 12wceq 1507 1 wff Vtx = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (1st𝑔), (Base‘𝑔)))
Colors of variables: wff setvar class
This definition is referenced by:  vtxval  26488
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