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Definition df-vtx 25921
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 25919 . 2 class Vtx
2 vg . . 3 setvar 𝑔
3 cvv 3231 . . 3 class V
42cv 1522 . . . . 5 class 𝑔
53, 3cxp 5141 . . . . 5 class (V × V)
64, 5wcel 2030 . . . 4 wff 𝑔 ∈ (V × V)
7 c1st 7208 . . . . 5 class 1st
84, 7cfv 5926 . . . 4 class (1st𝑔)
9 cbs 15904 . . . . 5 class Base
104, 9cfv 5926 . . . 4 class (Base‘𝑔)
116, 8, 10cif 4119 . . 3 class if(𝑔 ∈ (V × V), (1st𝑔), (Base‘𝑔))
122, 3, 11cmpt 4762 . 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (1st𝑔), (Base‘𝑔)))
131, 12wceq 1523 1 wff Vtx = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (1st𝑔), (Base‘𝑔)))
Colors of variables: wff setvar class
This definition is referenced by:  vtxval  25923  vtxvalOLD  25925
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