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Definition df-co 4297
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 , and calls the operation "relative product." (Contributed by NM, 4-Jul-1994.)
Assertion
Ref Expression
df-co (AB) = {⟨x, y⟩ ∣ z(xBz zAy)}
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 4292 . 2 class (AB)
4 vx . . . . . . 7 setvar x
54cv 1241 . . . . . 6 class x
6 vz . . . . . . 7 setvar z
76cv 1241 . . . . . 6 class z
85, 7, 2wbr 3755 . . . . 5 wff xBz
9 vy . . . . . . 7 setvar y
109cv 1241 . . . . . 6 class y
117, 10, 1wbr 3755 . . . . 5 wff zAy
128, 11wa 97 . . . 4 wff (xBz zAy)
1312, 6wex 1378 . . 3 wff z(xBz zAy)
1413, 4, 9copab 3808 . 2 class {⟨x, y⟩ ∣ z(xBz zAy)}
153, 14wceq 1242 1 wff (AB) = {⟨x, y⟩ ∣ z(xBz zAy)}
Colors of variables: wff set class
This definition is referenced by:  coss1  4434  coss2  4435  nfco  4444  brcog  4445  cnvco  4463  cotr  4649  relco  4762  coundi  4765  coundir  4766  cores  4767  xpcom  4807  dffun2  4855  funco  4883  xpcomco  6236
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