Definition df-co 4785

Description: Define the composition of two classes. Definition 6.6(3) of [TakeutiZaring] p. 24. Note that Definition 7 of [Suppes] p. 63 reverses A and B, uses a slash instead of o., and calls the operation "relative product". (Contributed by NM, 4-Jul-1994.)

Assertion

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

Distinct variable groups:   x, y, z, A   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 4780	. 2 class ( A o. B )
4		vx	. . . . . . 7 setvar x
5	4	cv 1401	. . . . . 6 class x
6		vz	. . . . . . 7 setvar z
7	6	cv 1401	. . . . . 6 class z
8	5, 7, 2	wbr 4131	. . . . 5 wff x B z
9		vy	. . . . . . 7 setvar y
10	9	cv 1401	. . . . . 6 class y
11	7, 10, 1	wbr 4131	. . . . 5 wff z A y
12	8, 11	wa 104	. . . 4 wff ( x B z /\ z A y )
13	12, 6	wex 1545	. . 3 wff E. z ( x B z /\ z A y )
14	13, 4, 9	copab 4192	. 2 class { <. x , y >. | E. z ( x B z /\ z A y ) }
15	3, 14	wceq 1402	1 wff ( A o. B ) = { <. x , y >. | E. z ( x B z /\ z A y ) }

This definition is used by:  coss1  4937  coss2  4938  nfco  4947  elco  4948  brcog  4949  cnvco  4967  cotr  5172  relco  5289  coundi  5292  coundir  5293  cores  5294  xpcom  5337  dffun2  5390  funco  5420  xpcomco  7128