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Definition df-in 3161
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 20814). Contrast this operation with union  ( A  u.  B
) (df-un 3159) and difference  ( A  \  B ) (df-dif 3157). For alternate definitions in terms of class difference, requiring no dummy variables, see dfin2 3407 and dfin4 3411. For intersection defined in terms of union, see dfin3 3410. (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 3153 . 2  class  ( A  i^i  B )
4 vx . . . . . 6  set  x
54cv 1624 . . . . 5  class  x
65, 1wcel 1686 . . . 4  wff  x  e.  A
75, 2wcel 1686 . . . 4  wff  x  e.  B
86, 7wa 358 . . 3  wff  ( x  e.  A  /\  x  e.  B )
98, 4cab 2271 . 2  class  { x  |  ( x  e.  A  /\  x  e.  B ) }
103, 9wceq 1625 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  3162  dfss2  3171  elin  3360  disj  3497  iinxprg  3981  disjex  23178  disjexc  23179  csbingVD  28733
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