MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-iin Structured version   Unicode version

Definition df-iin 4281
Description: Define indexed intersection. Definition of [Stoll] p. 45. See the remarks for its sibling operation of indexed union df-iun 4280. An alternate definition tying indexed intersection to ordinary intersection is dfiin2 4312. Theorem intiin 4331 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 4279 . 2  class  |^|_ x  e.  A  B
5 vy . . . . . 6  setvar  y
65cv 1369 . . . . 5  class  y
76, 3wcel 1758 . . . 4  wff  y  e.  B
87, 1, 2wral 2798 . . 3  wff  A. x  e.  A  y  e.  B
98, 5cab 2439 . 2  class  { y  |  A. x  e.  A  y  e.  B }
104, 9wceq 1370 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  4283  iineq1  4292  iineq2  4295  nfiin  4306  nfii1  4308  dfiin2g  4310  cbviin  4315  intiin  4331  0iin  4335  viin  4336  iinxsng  4354  iinxprg  4355  iinuni  4361  iineq12f  29124
  Copyright terms: Public domain W3C validator