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Definition df-in 3287
Description: Define the intersection of two classes. Definition 5.6 of [TakeutiZaring] p. 16. For example,  ( { 1 ,  3 }  i^i  { 1 ,  8 } )  =  { 1 } (ex-in 21686). Contrast this operation with union  ( A  u.  B
) (df-un 3285) and difference  ( A  \  B ) (df-dif 3283). For alternate definitions in terms of class difference, requiring no dummy variables, see dfin2 3537 and dfin4 3541. For intersection defined in terms of union, see dfin3 3540. (Contributed by NM, 29-Apr-1994.)
Assertion
Ref Expression
df-in  |-  ( A  i^i  B )  =  { x  |  ( x  e.  A  /\  x  e.  B ) }
Distinct variable groups:    x, A    x, B

Detailed syntax breakdown of Definition df-in
StepHypRef Expression
1 cA . . 3  class  A
2 cB . . 3  class  B
31, 2cin 3279 . 2  class  ( A  i^i  B )
4 vx . . . . . 6  set  x
54cv 1648 . . . . 5  class  x
65, 1wcel 1721 . . . 4  wff  x  e.  A
75, 2wcel 1721 . . . 4  wff  x  e.  B
86, 7wa 359 . . 3  wff  ( x  e.  A  /\  x  e.  B )
98, 4cab 2390 . 2  class  { x  |  ( x  e.  A  /\  x  e.  B ) }
103, 9wceq 1649 1  wff  ( A  i^i  B )  =  { x  |  ( x  e.  A  /\  x  e.  B ) }
Colors of variables: wff set class
This definition is referenced by:  dfin5  3288  dfss2  3297  elin  3490  disj  3628  iinxprg  4128  disjex  23985  disjexc  23986  csbingVD  28705
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