ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-int Structured version   GIF version

Definition df-int 3607
Description: Define the intersection of a class. Definition 7.35 of [TakeutiZaring] p. 44. For example, { { 1 , 3 } , { 1 , 8 } } = { 1 } . Compare this with the intersection of two classes, df-in 2918. (Contributed by NM, 18-Aug-1993.)
Assertion
Ref Expression
df-int A = {xy(y Ax y)}
Distinct variable group:   x,y,A

Detailed syntax breakdown of Definition df-int
StepHypRef Expression
1 cA . . 3 class A
21cint 3606 . 2 class A
3 vy . . . . . . 7 setvar y
43cv 1241 . . . . . 6 class y
54, 1wcel 1390 . . . . 5 wff y A
6 vx . . . . . 6 setvar x
76, 3wel 1391 . . . . 5 wff x y
85, 7wi 4 . . . 4 wff (y Ax y)
98, 3wal 1240 . . 3 wff y(y Ax y)
109, 6cab 2023 . 2 class {xy(y Ax y)}
112, 10wceq 1242 1 wff A = {xy(y Ax y)}
Colors of variables: wff set class
This definition is referenced by:  dfint2  3608  elint  3612  int0  3620  dfiin2g  3681  bdcint  9332  bdcriota  9338
  Copyright terms: Public domain W3C validator