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Definition df-in 2994
Description: Define the intersection of two classes. Definition 5.6 of [TakeutiZaring] p. 16. Contrast this operation with union  ( A  u.  B ) (df-un 2992) and difference  ( A  \  B ) (df-dif 2990). (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 2987 . 2  class  ( A  i^i  B )
4 vx . . . . . 6  setvar  x
54cv 1286 . . . . 5  class  x
65, 1wcel 1436 . . . 4  wff  x  e.  A
75, 2wcel 1436 . . . 4  wff  x  e.  B
86, 7wa 102 . . 3  wff  ( x  e.  A  /\  x  e.  B )
98, 4cab 2071 . 2  class  { x  |  ( x  e.  A  /\  x  e.  B ) }
103, 9wceq 1287 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  2995  dfss2  3003  elin  3172  disj  3319  iinxprg  3789  bdcin  11223
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