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Theorem viin 4389
Description: Indexed intersection with a universal index class. When doesn't depend on , this evaluates to by 19.3 1888 and abid2 2597. When , this evaluates to by intiin 4384 and intv 4628. (Contributed by NM, 11-Sep-2008.)
Assertion
Ref Expression
viin
Distinct variable groups:   ,   ,

Proof of Theorem viin
StepHypRef Expression
1 df-iin 4333 . 2
2 ralv 3123 . . 3
32abbii 2591 . 2
41, 3eqtri 2486 1
Colors of variables: wff setvar class
Syntax hints:  A.wal 1393  =wceq 1395  e.wcel 1818  {cab 2442  A.wral 2807   cvv 3109  |^|_ciin 4331
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-ral 2812  df-v 3111  df-iin 4333
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