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Definition df-funpart 32308
Description: Define the functional part of a class 𝐹. This is the maximal part of 𝐹 that is a function. See funpartfun 32377 and funpartfv 32379 for the meaning of this statement. (Contributed by Scott Fenton, 16-Apr-2014.)
Assertion
Ref Expression
df-funpart Funpart𝐹 = (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons )))

Detailed syntax breakdown of Definition df-funpart
StepHypRef Expression
1 cF . . 3 class 𝐹
21cfunpart 32283 . 2 class Funpart𝐹
31cimage 32274 . . . . . 6 class Image𝐹
4 csingle 32272 . . . . . 6 class Singleton
53, 4ccom 5270 . . . . 5 class (Image𝐹 ∘ Singleton)
6 cvv 3340 . . . . . 6 class V
7 csingles 32273 . . . . . 6 class Singletons
86, 7cxp 5264 . . . . 5 class (V × Singletons )
95, 8cin 3714 . . . 4 class ((Image𝐹 ∘ Singleton) ∩ (V × Singletons ))
109cdm 5266 . . 3 class dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons ))
111, 10cres 5268 . 2 class (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons )))
122, 11wceq 1632 1 wff Funpart𝐹 = (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons )))
Colors of variables: wff setvar class
This definition is referenced by:  funpartfun  32377  funpartss  32378  funpartfv  32379
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