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Definition df-in 3295
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 21694). Contrast this operation with union  ( A  u.  B
) (df-un 3293) and difference  ( A  \  B ) (df-dif 3291). For alternate definitions in terms of class difference, requiring no dummy variables, see dfin2 3545 and dfin4 3549. For intersection defined in terms of union, see dfin3 3548. (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 3287 . 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 2398 . 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  3296  dfss2  3305  elin  3498  disj  3636  iinxprg  4136  disjex  23993  disjexc  23994  csbingVD  28714
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