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Definition df-in 3270
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 21581). Contrast this operation with union  ( A  u.  B
) (df-un 3268) and difference  ( A  \  B ) (df-dif 3266). For alternate definitions in terms of class difference, requiring no dummy variables, see dfin2 3520 and dfin4 3524. For intersection defined in terms of union, see dfin3 3523. (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 3262 . 2  class  ( A  i^i  B )
4 vx . . . . . 6  set  x
54cv 1648 . . . . 5  class  x
65, 1wcel 1717 . . . 4  wff  x  e.  A
75, 2wcel 1717 . . . 4  wff  x  e.  B
86, 7wa 359 . . 3  wff  ( x  e.  A  /\  x  e.  B )
98, 4cab 2373 . 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  3271  dfss2  3280  elin  3473  disj  3611  iinxprg  4109  disjex  23875  disjexc  23876  csbingVD  28337
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