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Definition df-vtx 28883
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 28881 . 2 class Vtx
2 vg . . 3 setvar 𝑔
3 cvv 3461 . . 3 class V
42cv 1532 . . . . 5 class 𝑔
53, 3cxp 5676 . . . . 5 class (V × V)
64, 5wcel 2098 . . . 4 wff 𝑔 ∈ (V × V)
7 c1st 7992 . . . . 5 class 1st
84, 7cfv 6549 . . . 4 class (1st𝑔)
9 cbs 17183 . . . . 5 class Base
104, 9cfv 6549 . . . 4 class (Base‘𝑔)
116, 8, 10cif 4530 . . 3 class if(𝑔 ∈ (V × V), (1st𝑔), (Base‘𝑔))
122, 3, 11cmpt 5232 . 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (1st𝑔), (Base‘𝑔)))
131, 12wceq 1533 1 wff Vtx = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (1st𝑔), (Base‘𝑔)))
Colors of variables: wff setvar class
This definition is referenced by:  vtxval  28885
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