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Definition df-in 3045
Description: Define the intersection of two classes. Definition 5.6 of [TakeutiZaring] p. 16. Contrast this operation with union  ( A  u.  B ) (df-un 3043) and difference  ( A  \  B ) (df-dif 3041). (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 3038 . 2  class  ( A  i^i  B )
4 vx . . . . . 6  setvar  x
54cv 1313 . . . . 5  class  x
65, 1wcel 1463 . . . 4  wff  x  e.  A
75, 2wcel 1463 . . . 4  wff  x  e.  B
86, 7wa 103 . . 3  wff  ( x  e.  A  /\  x  e.  B )
98, 4cab 2101 . 2  class  { x  |  ( x  e.  A  /\  x  e.  B ) }
103, 9wceq 1314 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  3046  dfss2  3054  elin  3227  disj  3379  iinxprg  3855  bdcin  12895
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