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Definition df-fullfun 32309
Description: Define the full function over 𝐹. This is a function with domain V that always agrees with 𝐹 for its value. (Contributed by Scott Fenton, 17-Apr-2014.)
Assertion
Ref Expression
df-fullfun FullFun𝐹 = (Funpart𝐹 ∪ ((V ∖ dom Funpart𝐹) × {∅}))

Detailed syntax breakdown of Definition df-fullfun
StepHypRef Expression
1 cF . . 3 class 𝐹
21cfullfn 32284 . 2 class FullFun𝐹
31cfunpart 32283 . . 3 class Funpart𝐹
4 cvv 3340 . . . . 5 class V
53cdm 5266 . . . . 5 class dom Funpart𝐹
64, 5cdif 3712 . . . 4 class (V ∖ dom Funpart𝐹)
7 c0 4058 . . . . 5 class
87csn 4321 . . . 4 class {∅}
96, 8cxp 5264 . . 3 class ((V ∖ dom Funpart𝐹) × {∅})
103, 9cun 3713 . 2 class (Funpart𝐹 ∪ ((V ∖ dom Funpart𝐹) × {∅}))
112, 10wceq 1632 1 wff FullFun𝐹 = (Funpart𝐹 ∪ ((V ∖ dom Funpart𝐹) × {∅}))
Colors of variables: wff setvar class
This definition is referenced by:  fullfunfnv  32380  fullfunfv  32381
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