Definition df-funpart 34841

Description: Define the functional part of a class 𝐹. This is the maximal part of 𝐹 that is a function. See funpartfun 34910 and funpartfv 34912 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

Step	Hyp	Ref	Expression
1		cF	. . 3 class 𝐹
2	1	cfunpart 34816	. 2 class Funpart𝐹
3	1	cimage 34807	. . . . . 6 class Image𝐹
4		csingle 34805	. . . . . 6 class Singleton
5	3, 4	ccom 5680	. . . . 5 class (Image𝐹 ∘ Singleton)
6		cvv 3474	. . . . . 6 class V
7		csingles 34806	. . . . . 6 class Singletons
8	6, 7	cxp 5674	. . . . 5 class (V × Singletons )
9	5, 8	cin 3947	. . . 4 class ((Image𝐹 ∘ Singleton) ∩ (V × Singletons ))
10	9	cdm 5676	. . 3 class dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons ))
11	1, 10	cres 5678	. 2 class (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons )))
12	2, 11	wceq 1541	1 wff Funpart𝐹 = (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons )))

This definition is referenced by:  funpartfun  34910  funpartss  34911  funpartfv  34912