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Definition df-iedg 26798
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 26796 . 2 class iEdg
2 vg . . 3 setvar 𝑔
3 cvv 3480 . . 3 class V
42cv 1537 . . . . 5 class 𝑔
53, 3cxp 5540 . . . . 5 class (V × V)
64, 5wcel 2115 . . . 4 wff 𝑔 ∈ (V × V)
7 c2nd 7683 . . . . 5 class 2nd
84, 7cfv 6343 . . . 4 class (2nd𝑔)
9 cedgf 26788 . . . . 5 class .ef
104, 9cfv 6343 . . . 4 class (.ef‘𝑔)
116, 8, 10cif 4450 . . 3 class if(𝑔 ∈ (V × V), (2nd𝑔), (.ef‘𝑔))
122, 3, 11cmpt 5132 . 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd𝑔), (.ef‘𝑔)))
131, 12wceq 1538 1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd𝑔), (.ef‘𝑔)))
Colors of variables: wff setvar class
This definition is referenced by:  iedgval  26800
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