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Definition df-in 3085
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 20625). Contrast this operation with union  ( A  u.  B
) (df-un 3083) and difference  ( A  \  B ) (df-dif 3081). For alternate definitions in terms of class difference, requiring no dummy variables, see dfin2 3312 and dfin4 3316. For intersection defined in terms of union, see dfin3 3315. (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 3077 . 2  class  ( A  i^i  B )
4 vx . . . . . 6  set  x
54cv 1618 . . . . 5  class  x
65, 1wcel 1621 . . . 4  wff  x  e.  A
75, 2wcel 1621 . . . 4  wff  x  e.  B
86, 7wa 360 . . 3  wff  ( x  e.  A  /\  x  e.  B )
98, 4cab 2239 . 2  class  { x  |  ( x  e.  A  /\  x  e.  B ) }
103, 9wceq 1619 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  3086  dfss2  3092  elin  3266  disj  3402  iinxprg  3877  csbingVD  27350
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