Definition df-supp 7296

Description: Define the support of a function against a "zero" value. According to Wikipedia ("Support (mathematics)", 31-Mar-2019, https://en.wikipedia.org/wiki/Support_(mathematics)) "In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero." and "The notion of support also extends in a natural way to functions taking values in more general sets than R [the real numbers] and to other objects.". The following definition allows for such extensions, being applicable for any sets (which usually are functions) and any element (even not necessarily from the range of the function) regarded as "zero". (Contributed by AV, 31-Mar-2019.) (Revised by AV, 6-Apr-2019.)

Assertion

Ref	Expression
df-supp	|- supp = ( x e. _V , z e. _V |-> { i e. dom x | ( x " { i } ) =/= { z } } )

Distinct variable group:   x, i, z

Detailed syntax breakdown of Definition df-supp

Step	Hyp	Ref	Expression
1		csupp 7295	. 2 class supp
2		vx	. . 3 setvar x
3		vz	. . 3 setvar z
4		cvv 3200	. . 3 class _V
5	2	cv 1482	. . . . . 6 class x
6		vi	. . . . . . . 8 setvar i
7	6	cv 1482	. . . . . . 7 class i
8	7	csn 4177	. . . . . 6 class { i }
9	5, 8	cima 5117	. . . . 5 class ( x " { i } )
10	3	cv 1482	. . . . . 6 class z
11	10	csn 4177	. . . . 5 class { z }
12	9, 11	wne 2794	. . . 4 wff ( x " { i } ) =/= { z }
13	5	cdm 5114	. . . 4 class dom x
14	12, 6, 13	crab 2916	. . 3 class { i e. dom x | ( x " { i } ) =/= { z } }
15	2, 3, 4, 4, 14	cmpt2 6652	. 2 class ( x e. _V , z e. _V |-> { i e. dom x | ( x " { i } ) =/= { z } } )
16	1, 15	wceq 1483	1 wff supp = ( x e. _V , z e. _V |-> { i e. dom x | ( x " { i } ) =/= { z } } )

This definition is referenced by:  suppval  7297  supp0prc  7298