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Definition df-in 3319
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 21725). Contrast this operation with union  ( A  u.  B
) (df-un 3317) and difference  ( A  \  B ) (df-dif 3315). For alternate definitions in terms of class difference, requiring no dummy variables, see dfin2 3569 and dfin4 3573. For intersection defined in terms of union, see dfin3 3572. (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 3311 . 2  class  ( A  i^i  B )
4 vx . . . . . 6  set  x
54cv 1651 . . . . 5  class  x
65, 1wcel 1725 . . . 4  wff  x  e.  A
75, 2wcel 1725 . . . 4  wff  x  e.  B
86, 7wa 359 . . 3  wff  ( x  e.  A  /\  x  e.  B )
98, 4cab 2421 . 2  class  { x  |  ( x  e.  A  /\  x  e.  B ) }
103, 9wceq 1652 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  3320  dfss2  3329  elin  3522  disj  3660  iinxprg  4160  disjex  24024  disjexc  24025  csbingVD  28933
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