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Definition df-int 3663
Description: Define the intersection of a class. Definition 7.35 of [TakeutiZaring] p. 44. For example,  |^| { { 1 , 3 } , { 1 , 8 } } = { 1 } . Compare this with the intersection of two classes, df-in 2990. (Contributed by NM, 18-Aug-1993.)
Assertion
Ref Expression
df-int  |-  |^| A  =  { x  |  A. y ( y  e.  A  ->  x  e.  y ) }
Distinct variable group:    x, y, A

Detailed syntax breakdown of Definition df-int
StepHypRef Expression
1 cA . . 3  class  A
21cint 3662 . 2  class  |^| A
3 vy . . . . . . 7  setvar  y
43cv 1284 . . . . . 6  class  y
54, 1wcel 1434 . . . . 5  wff  y  e.  A
6 vx . . . . . 6  setvar  x
76, 3wel 1435 . . . . 5  wff  x  e.  y
85, 7wi 4 . . . 4  wff  ( y  e.  A  ->  x  e.  y )
98, 3wal 1283 . . 3  wff  A. y
( y  e.  A  ->  x  e.  y )
109, 6cab 2069 . 2  class  { x  |  A. y ( y  e.  A  ->  x  e.  y ) }
112, 10wceq 1285 1  wff  |^| A  =  { x  |  A. y ( y  e.  A  ->  x  e.  y ) }
Colors of variables: wff set class
This definition is referenced by:  dfint2  3664  elint  3668  int0  3676  dfiin2g  3737  bdcint  11111  bdcriota  11117
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