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Definition df-iedg 26351
Description: Define the function mapping a graph to its indexed edges. This definition is very general: It defines the indexed edges for any ordered pair as its second component, and for any other class as its "edge function". It is meaningful, however, only if the ordered pair represents a graph resp. the class is an extensible structure (containing a slot for "edge functions") representing a graph. (Contributed by AV, 20-Sep-2020.)
Assertion
Ref Expression
df-iedg iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd𝑔), (.ef‘𝑔)))

Detailed syntax breakdown of Definition df-iedg
StepHypRef Expression
1 ciedg 26349 . 2 class iEdg
2 vg . . 3 setvar 𝑔
3 cvv 3398 . . 3 class V
42cv 1600 . . . . 5 class 𝑔
53, 3cxp 5355 . . . . 5 class (V × V)
64, 5wcel 2107 . . . 4 wff 𝑔 ∈ (V × V)
7 c2nd 7446 . . . . 5 class 2nd
84, 7cfv 6137 . . . 4 class (2nd𝑔)
9 cedgf 26341 . . . . 5 class .ef
104, 9cfv 6137 . . . 4 class (.ef‘𝑔)
116, 8, 10cif 4307 . . 3 class if(𝑔 ∈ (V × V), (2nd𝑔), (.ef‘𝑔))
122, 3, 11cmpt 4967 . 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd𝑔), (.ef‘𝑔)))
131, 12wceq 1601 1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd𝑔), (.ef‘𝑔)))
Colors of variables: wff setvar class
This definition is referenced by:  iedgval  26353
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