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Definition df-in 3159
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 20812). Contrast this operation with union  ( A  u.  B
) (df-un 3157) and difference  ( A  \  B ) (df-dif 3155). For alternate definitions in terms of class difference, requiring no dummy variables, see dfin2 3405 and dfin4 3409. For intersection defined in terms of union, see dfin3 3408. (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 3151 . 2  class  ( A  i^i  B )
4 vx . . . . . 6  set  x
54cv 1622 . . . . 5  class  x
65, 1wcel 1684 . . . 4  wff  x  e.  A
75, 2wcel 1684 . . . 4  wff  x  e.  B
86, 7wa 358 . . 3  wff  ( x  e.  A  /\  x  e.  B )
98, 4cab 2269 . 2  class  { x  |  ( x  e.  A  /\  x  e.  B ) }
103, 9wceq 1623 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  3160  dfss2  3169  elin  3358  disj  3495  iinxprg  3979  disjex  23176  disjexc  23177  csbingVD  28660
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