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Definition df-iedg 28805
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 28803 . 2 class iEdg
2 vg . . 3 setvar 𝑔
3 cvv 3469 . . 3 class V
42cv 1533 . . . . 5 class 𝑔
53, 3cxp 5670 . . . . 5 class (V × V)
64, 5wcel 2099 . . . 4 wff 𝑔 ∈ (V × V)
7 c2nd 7986 . . . . 5 class 2nd
84, 7cfv 6542 . . . 4 class (2nd𝑔)
9 cedgf 28792 . . . . 5 class .ef
104, 9cfv 6542 . . . 4 class (.ef‘𝑔)
116, 8, 10cif 4524 . . 3 class if(𝑔 ∈ (V × V), (2nd𝑔), (.ef‘𝑔))
122, 3, 11cmpt 5225 . 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd𝑔), (.ef‘𝑔)))
131, 12wceq 1534 1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd𝑔), (.ef‘𝑔)))
Colors of variables: wff setvar class
This definition is referenced by:  iedgval  28807
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