Definition df-funpart 33760

Description: Define the functional part of a class 𝐹. This is the maximal part of 𝐹 that is a function. See funpartfun 33829 and funpartfv 33831 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 33735	. 2 class Funpart𝐹
3	1	cimage 33726	. . . . . 6 class Image𝐹
4		csingle 33724	. . . . . 6 class Singleton
5	3, 4	ccom 5532	. . . . 5 class (Image𝐹 ∘ Singleton)
6		cvv 3409	. . . . . 6 class V
7		csingles 33725	. . . . . 6 class Singletons
8	6, 7	cxp 5526	. . . . 5 class (V × Singletons )
9	5, 8	cin 3859	. . . 4 class ((Image𝐹 ∘ Singleton) ∩ (V × Singletons ))
10	9	cdm 5528	. . 3 class dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons ))
11	1, 10	cres 5530	. 2 class (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons )))
12	2, 11	wceq 1538	1 wff Funpart𝐹 = (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons )))

This definition is referenced by:  funpartfun  33829  funpartss  33830  funpartfv  33831