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Definition df-in 3160
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 20787). Contrast this operation with union  ( A  u.  B
) (df-un 3158) and difference  ( A  \  B ) (df-dif 3156). For alternate definitions in terms of class difference, requiring no dummy variables, see dfin2 3406 and dfin4 3410. For intersection defined in terms of union, see dfin3 3409. (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 3152 . 2  class  ( A  i^i  B )
4 vx . . . . . 6  set  x
54cv 1623 . . . . 5  class  x
65, 1wcel 1685 . . . 4  wff  x  e.  A
75, 2wcel 1685 . . . 4  wff  x  e.  B
86, 7wa 360 . . 3  wff  ( x  e.  A  /\  x  e.  B )
98, 4cab 2270 . 2  class  { x  |  ( x  e.  A  /\  x  e.  B ) }
103, 9wceq 1624 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  3161  dfss2  3170  elin  3359  disj  3496  iinxprg  3980  csbingVD  27928
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