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Definition df-iedg 25922
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 25920 . 2 class iEdg
2 vg . . 3 setvar 𝑔
3 cvv 3231 . . 3 class V
42cv 1522 . . . . 5 class 𝑔
53, 3cxp 5141 . . . . 5 class (V × V)
64, 5wcel 2030 . . . 4 wff 𝑔 ∈ (V × V)
7 c2nd 7209 . . . . 5 class 2nd
84, 7cfv 5926 . . . 4 class (2nd𝑔)
9 cedgf 25912 . . . . 5 class .ef
104, 9cfv 5926 . . . 4 class (.ef‘𝑔)
116, 8, 10cif 4119 . . 3 class if(𝑔 ∈ (V × V), (2nd𝑔), (.ef‘𝑔))
122, 3, 11cmpt 4762 . 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd𝑔), (.ef‘𝑔)))
131, 12wceq 1523 1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd𝑔), (.ef‘𝑔)))
Colors of variables: wff setvar class
This definition is referenced by:  iedgval  25924  iedgvalOLD  25926
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