Definition df-image 35865

Description: Define the image functor. This function takes a set 𝐴 to a function 𝑥 ↦ (𝐴 “ 𝑥), providing that the latter exists. See imageval 35931 for the derivation. (Contributed by Scott Fenton, 27-Mar-2014.)

Assertion

Ref	Expression
df-image	⊢ Image𝐴 = ((V × V) ∖ ran ((V ⊗ E ) △ (( E ∘ ◡𝐴) ⊗ V)))

Detailed syntax breakdown of Definition df-image

Step	Hyp	Ref	Expression
1		cA	. . 3 class 𝐴
2	1	cimage 35841	. 2 class Image𝐴
3		cvv 3480	. . . 4 class V
4	3, 3	cxp 5683	. . 3 class (V × V)
5		cep 5583	. . . . . 6 class E
6	3, 5	ctxp 35831	. . . . 5 class (V ⊗ E )
7	1	ccnv 5684	. . . . . . 7 class ◡𝐴
8	5, 7	ccom 5689	. . . . . 6 class ( E ∘ ◡𝐴)
9	8, 3	ctxp 35831	. . . . 5 class (( E ∘ ◡𝐴) ⊗ V)
10	6, 9	csymdif 4252	. . . 4 class ((V ⊗ E ) △ (( E ∘ ◡𝐴) ⊗ V))
11	10	crn 5686	. . 3 class ran ((V ⊗ E ) △ (( E ∘ ◡𝐴) ⊗ V))
12	4, 11	cdif 3948	. 2 class ((V × V) ∖ ran ((V ⊗ E ) △ (( E ∘ ◡𝐴) ⊗ V)))
13	2, 12	wceq 1540	1 wff Image𝐴 = ((V × V) ∖ ran ((V ⊗ E ) △ (( E ∘ ◡𝐴) ⊗ V)))

This definition is referenced by:  brimage  35927  funimage  35929