Definition df-funpart 36372

Description: Define the functional part of a class 𝐹. This is the maximal part of 𝐹 that is a function. See funpartfun 36443 and funpartfv 36445 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 36347	. 2 class Funpart𝐹
3	1	cimage 36338	. . . . . 6 class Image𝐹
4		csingle 36336	. . . . . 6 class Singleton
5	3, 4	ccom 5664	. . . . 5 class (Image𝐹 ∘ Singleton)
6		cvv 3454	. . . . . 6 class V
7		csingles 36337	. . . . . 6 class Singletons
8	6, 7	cxp 5658	. . . . 5 class (V × Singletons )
9	5, 8	cin 3903	. . . 4 class ((Image𝐹 ∘ Singleton) ∩ (V × Singletons ))
10	9	cdm 5660	. . 3 class dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons ))
11	1, 10	cres 5662	. 2 class (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons )))
12	2, 11	wceq 1569	1 wff Funpart𝐹 = (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons )))

This definition is used by:  funpartfun  36443  funpartss  36444  funpartfv  36445