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Definition df-vtx 26800
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 26798 . 2 class Vtx
2 vg . . 3 setvar 𝑔
3 cvv 3480 . . 3 class V
42cv 1537 . . . . 5 class 𝑔
53, 3cxp 5541 . . . . 5 class (V × V)
64, 5wcel 2115 . . . 4 wff 𝑔 ∈ (V × V)
7 c1st 7684 . . . . 5 class 1st
84, 7cfv 6345 . . . 4 class (1st𝑔)
9 cbs 16485 . . . . 5 class Base
104, 9cfv 6345 . . . 4 class (Base‘𝑔)
116, 8, 10cif 4450 . . 3 class if(𝑔 ∈ (V × V), (1st𝑔), (Base‘𝑔))
122, 3, 11cmpt 5133 . 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (1st𝑔), (Base‘𝑔)))
131, 12wceq 1538 1 wff Vtx = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (1st𝑔), (Base‘𝑔)))
Colors of variables: wff setvar class
This definition is referenced by:  vtxval  26802
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