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Definition df-iin 4305
Description: Define indexed intersection. Definition of [Stoll] p. 45. See the remarks for its sibling operation of indexed union df-iun 4304. An alternate definition tying indexed intersection to ordinary intersection is dfiin2 4337. Theorem intiin 4356 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 4303 . 2  class  |^|_ x  e.  A  B
5 vy . . . . . 6  setvar  y
65cv 1436 . . . . 5  class  y
76, 3wcel 1870 . . . 4  wff  y  e.  B
87, 1, 2wral 2782 . . 3  wff  A. x  e.  A  y  e.  B
98, 5cab 2414 . 2  class  { y  |  A. x  e.  A  y  e.  B }
104, 9wceq 1437 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  4308  iineq1  4317  iineq2  4320  nfiin  4331  nfii1  4333  dfiin2g  4335  cbviin  4340  intiin  4356  0iin  4360  viin  4361  iinxsng  4382  iinxprg  4383  iinuni  4389  iineq12f  32111
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