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Definition df-in 3235
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 20918). Contrast this operation with union  ( A  u.  B
) (df-un 3233) and difference  ( A  \  B ) (df-dif 3231). For alternate definitions in terms of class difference, requiring no dummy variables, see dfin2 3481 and dfin4 3485. For intersection defined in terms of union, see dfin3 3484. (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 3227 . 2  class  ( A  i^i  B )
4 vx . . . . . 6  set  x
54cv 1641 . . . . 5  class  x
65, 1wcel 1710 . . . 4  wff  x  e.  A
75, 2wcel 1710 . . . 4  wff  x  e.  B
86, 7wa 358 . . 3  wff  ( x  e.  A  /\  x  e.  B )
98, 4cab 2344 . 2  class  { x  |  ( x  e.  A  /\  x  e.  B ) }
103, 9wceq 1642 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  3236  dfss2  3245  elin  3434  disj  3571  iinxprg  4058  disjex  23227  disjexc  23228  csbingVD  28405
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