Definition df-co 4726

Description: Define the composition of two classes. (Contributed by SF, 5-Jan-2015.)

Assertion

Ref	Expression
df-co	|- (A o. B) = {<.x, y>. | E.z(xBz /\ zAy)}

Distinct variable groups:   x,A,y,z   x,B,y,z

Detailed syntax breakdown of Definition df-co

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cB	. . 3 class B
3	1, 2	ccom 4721	. 2 class (A o. B)
4		vx	. . . . . . 7 setvar x
5	4	cv 1641	. . . . . 6 class x
6		vz	. . . . . . 7 setvar z
7	6	cv 1641	. . . . . 6 class z
8	5, 7, 2	wbr 4639	. . . . 5 wff xBz
9		vy	. . . . . . 7 setvar y
10	9	cv 1641	. . . . . 6 class y
11	7, 10, 1	wbr 4639	. . . . 5 wff zAy
12	8, 11	wa 358	. . . 4 wff (xBz /\ zAy)
13	12, 6	wex 1541	. . 3 wff E.z(xBz /\ zAy)
14	13, 4, 9	copab 4622	. 2 class {<.x, y>. | E.z(xBz /\ zAy)}
15	3, 14	wceq 1642	1 wff (A o. B) = {<.x, y>. | E.z(xBz /\ zAy)}

This definition is referenced by:  dfco1  4748  coss1  4872  coss2  4873  nfco  4882  brco  4883  cnvco  4894  coundi  5082  coundir  5083  cores  5084  df2nd2  5111  funco  5142  composeex  5820