ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-co Unicode version

Definition df-co 4381
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
StepHypRef Expression
1 cA . . 3  class  A
2 cB . . 3  class  B
31, 2ccom 4376 . 2  class  ( A  o.  B )
4 vx . . . . . . 7  setvar  x
54cv 1258 . . . . . 6  class  x
6 vz . . . . . . 7  setvar  z
76cv 1258 . . . . . 6  class  z
85, 7, 2wbr 3791 . . . . 5  wff  x B z
9 vy . . . . . . 7  setvar  y
109cv 1258 . . . . . 6  class  y
117, 10, 1wbr 3791 . . . . 5  wff  z A y
128, 11wa 101 . . . 4  wff  ( x B z  /\  z A y )
1312, 6wex 1397 . . 3  wff  E. z
( x B z  /\  z A y )
1413, 4, 9copab 3844 . 2  class  { <. x ,  y >.  |  E. z ( x B z  /\  z A y ) }
153, 14wceq 1259 1  wff  ( A  o.  B )  =  { <. x ,  y
>.  |  E. z
( x B z  /\  z A y ) }
Colors of variables: wff set class
This definition is referenced by:  coss1  4518  coss2  4519  nfco  4528  brcog  4529  cnvco  4547  cotr  4733  relco  4846  coundi  4849  coundir  4850  cores  4851  xpcom  4891  dffun2  4939  funco  4967  xpcomco  6330
  Copyright terms: Public domain W3C validator