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Definition df-iin 4169
Description: Define indexed intersection. Definition of [Stoll] p. 45. See the remarks for its sibling operation of indexed union df-iun 4168. An alternate definition tying indexed intersection to ordinary intersection is dfiin2 4200. Theorem intiin 4219 provides a definition of ordinary intersection in terms of indexed intersection. (Contributed by NM, 27-Jun-1998.)
Assertion
Ref Expression
df-iin  |-  |^|_ x  e.  A  B  =  { y  |  A. x  e.  A  y  e.  B }
Distinct variable groups:    x, y    y, A    y, B
Allowed substitution hints:    A( x)    B( x)

Detailed syntax breakdown of Definition df-iin
StepHypRef Expression
1 vx . . 3  setvar  x
2 cA . . 3  class  A
3 cB . . 3  class  B
41, 2, 3ciin 4167 . 2  class  |^|_ x  e.  A  B
5 vy . . . . . 6  setvar  y
65cv 1368 . . . . 5  class  y
76, 3wcel 1756 . . . 4  wff  y  e.  B
87, 1, 2wral 2710 . . 3  wff  A. x  e.  A  y  e.  B
98, 5cab 2424 . 2  class  { y  |  A. x  e.  A  y  e.  B }
104, 9wceq 1369 1  wff  |^|_ x  e.  A  B  =  { y  |  A. x  e.  A  y  e.  B }
Colors of variables: wff setvar class
This definition is referenced by:  eliin  4171  iineq1  4180  iineq2  4183  nfiin  4194  nfii1  4196  dfiin2g  4198  cbviin  4203  intiin  4219  0iin  4223  viin  4224  iinxsng  4242  iinxprg  4243  iinuni  4249  iineq12f  28948
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