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Definition df-in 3316
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 21771). Contrast this operation with union  ( A  u.  B
) (df-un 3314) and difference  ( A  \  B ) (df-dif 3312). For alternate definitions in terms of class difference, requiring no dummy variables, see dfin2 3565 and dfin4 3569. For intersection defined in terms of union, see dfin3 3568. (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 3308 . 2  class  ( A  i^i  B )
4 vx . . . . . 6  set  x
54cv 1653 . . . . 5  class  x
65, 1wcel 1728 . . . 4  wff  x  e.  A
75, 2wcel 1728 . . . 4  wff  x  e.  B
86, 7wa 360 . . 3  wff  ( x  e.  A  /\  x  e.  B )
98, 4cab 2429 . 2  class  { x  |  ( x  e.  A  /\  x  e.  B ) }
103, 9wceq 1654 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  3317  dfss2  3326  elin  3519  disj  3696  iinxprg  4199  disjex  24067  disjexc  24068  csbingVD  29170
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