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Definition df-vtx 26710
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 26708 . 2 class Vtx
2 vg . . 3 setvar 𝑔
3 cvv 3492 . . 3 class V
42cv 1527 . . . . 5 class 𝑔
53, 3cxp 5546 . . . . 5 class (V × V)
64, 5wcel 2105 . . . 4 wff 𝑔 ∈ (V × V)
7 c1st 7676 . . . . 5 class 1st
84, 7cfv 6348 . . . 4 class (1st𝑔)
9 cbs 16471 . . . . 5 class Base
104, 9cfv 6348 . . . 4 class (Base‘𝑔)
116, 8, 10cif 4463 . . 3 class if(𝑔 ∈ (V × V), (1st𝑔), (Base‘𝑔))
122, 3, 11cmpt 5137 . 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (1st𝑔), (Base‘𝑔)))
131, 12wceq 1528 1 wff Vtx = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (1st𝑔), (Base‘𝑔)))
Colors of variables: wff setvar class
This definition is referenced by:  vtxval  26712
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