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Definition df-in 3291
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 21690). Contrast this operation with union  ( A  u.  B
) (df-un 3289) and difference  ( A  \  B ) (df-dif 3287). For alternate definitions in terms of class difference, requiring no dummy variables, see dfin2 3541 and dfin4 3545. For intersection defined in terms of union, see dfin3 3544. (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 3283 . 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 2394 . 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  3292  dfss2  3301  elin  3494  disj  3632  iinxprg  4132  disjex  23989  disjexc  23990  csbingVD  28709
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