Definition df-funpart 35897

Description: Define the functional part of a class 𝐹. This is the maximal part of 𝐹 that is a function. See funpartfun 35966 and funpartfv 35968 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 35872	. 2 class Funpart𝐹
3	1	cimage 35863	. . . . . 6 class Image𝐹
4		csingle 35861	. . . . . 6 class Singleton
5	3, 4	ccom 5663	. . . . 5 class (Image𝐹 ∘ Singleton)
6		cvv 3464	. . . . . 6 class V
7		csingles 35862	. . . . . 6 class Singletons
8	6, 7	cxp 5657	. . . . 5 class (V × Singletons )
9	5, 8	cin 3930	. . . 4 class ((Image𝐹 ∘ Singleton) ∩ (V × Singletons ))
10	9	cdm 5659	. . 3 class dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons ))
11	1, 10	cres 5661	. 2 class (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons )))
12	2, 11	wceq 1540	1 wff Funpart𝐹 = (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons )))

This definition is referenced by:  funpartfun  35966  funpartss  35967  funpartfv  35968