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Definition df-in 3328
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 21734). Contrast this operation with union  ( A  u.  B
) (df-un 3326) and difference  ( A  \  B ) (df-dif 3324). For alternate definitions in terms of class difference, requiring no dummy variables, see dfin2 3578 and dfin4 3582. For intersection defined in terms of union, see dfin3 3581. (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 3320 . 2  class  ( A  i^i  B )
4 vx . . . . . 6  set  x
54cv 1652 . . . . 5  class  x
65, 1wcel 1726 . . . 4  wff  x  e.  A
75, 2wcel 1726 . . . 4  wff  x  e.  B
86, 7wa 360 . . 3  wff  ( x  e.  A  /\  x  e.  B )
98, 4cab 2423 . 2  class  { x  |  ( x  e.  A  /\  x  e.  B ) }
103, 9wceq 1653 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  3329  dfss2  3338  elin  3531  disj  3669  iinxprg  4169  disjex  24033  disjexc  24034  csbingVD  28997
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