Definition df-ofc 30158

Description: Define the function/constant operation map. The definition is designed so that if R is a binary operation, then ∘_𝑓/𝑐 R is the analogous operation on functions and constants. (Contributed by Thierry Arnoux, 21-Jan-2017.)

Assertion

Ref	Expression
df-ofc	|- ∘𝑓/𝑐 R = ( f e. _V , c e. _V |-> ( x e. dom f |-> ( ( f ` x ) R c ) ) )

Distinct variable group:   f, c, x, R

Detailed syntax breakdown of Definition df-ofc

Step	Hyp	Ref	Expression
1		cR	. . 3 class R
2	1	cofc 30157	. 2 class ∘𝑓/𝑐 R
3		vf	. . 3 setvar f
4		vc	. . 3 setvar c
5		cvv 3200	. . 3 class _V
6		vx	. . . 4 setvar x
7	3	cv 1482	. . . . 5 class f
8	7	cdm 5114	. . . 4 class dom f
9	6	cv 1482	. . . . . 6 class x
10	9, 7	cfv 5888	. . . . 5 class ( f ` x )
11	4	cv 1482	. . . . 5 class c
12	10, 11, 1	co 6650	. . . 4 class ( ( f ` x ) R c )
13	6, 8, 12	cmpt 4729	. . 3 class ( x e. dom f |-> ( ( f ` x ) R c ) )
14	3, 4, 5, 5, 13	cmpt2 6652	. 2 class ( f e. _V , c e. _V |-> ( x e. dom f |-> ( ( f ` x ) R c ) ) )
15	2, 14	wceq 1483	1 wff ∘𝑓/𝑐 R = ( f e. _V , c e. _V |-> ( x e. dom f |-> ( ( f ` x ) R c ) ) )

This definition is referenced by:  ofceq  30159  ofcfval  30160  ofcfval3  30164