Definition df-image 31971

Description: Define the image functor. This function takes a set A to a function x |-> ( A " x ), providing that the latter exists. See imageval 32037 for the derivation. (Contributed by Scott Fenton, 27-Mar-2014.)

Assertion

Ref	Expression
df-image	|- Image A = ( ( _V X. _V ) \ ran ( ( _V (x) _E ) /_\ ( ( _E o. `' A ) (x) _V ) ) )

Detailed syntax breakdown of Definition df-image

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2	1	cimage 31947	. 2 class Image A
3		cvv 3200	. . . 4 class _V
4	3, 3	cxp 5112	. . 3 class ( _V X. _V )
5		cep 5028	. . . . . 6 class _E
6	3, 5	ctxp 31937	. . . . 5 class ( _V (x) _E )
7	1	ccnv 5113	. . . . . . 7 class `' A
8	5, 7	ccom 5118	. . . . . 6 class ( _E o. `' A )
9	8, 3	ctxp 31937	. . . . 5 class ( ( _E o. `' A ) (x) _V )
10	6, 9	csymdif 3843	. . . 4 class ( ( _V (x) _E ) /_\ ( ( _E o. `' A ) (x) _V ) )
11	10	crn 5115	. . 3 class ran ( ( _V (x) _E ) /_\ ( ( _E o. `' A ) (x) _V ) )
12	4, 11	cdif 3571	. 2 class ( ( _V X. _V ) \ ran ( ( _V (x) _E ) /_\ ( ( _E o. `' A ) (x) _V ) ) )
13	2, 12	wceq 1483	1 wff Image A = ( ( _V X. _V ) \ ran ( ( _V (x) _E ) /_\ ( ( _E o. `' A ) (x) _V ) ) )

This definition is referenced by:  brimage  32033  funimage  32035