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Theorem viin 4025
 Description: Indexed intersection with a universal index class. When A doesn't depend on x, this evaluates to A by 19.3 1785 and abid2 2470. When A = x, this evaluates to ∅ by intiin 4020 and intv in set.mm. (Contributed by NM, 11-Sep-2008.)
Assertion
Ref Expression
viin x V A = {y x y A}
Distinct variable groups:   x,y   y,A
Allowed substitution hint:   A(x)

Proof of Theorem viin
StepHypRef Expression
1 df-iin 3972 . 2 x V A = {y x V y A}
2 ralv 2872 . . 3 (x V y Ax y A)
32abbii 2465 . 2 {y x V y A} = {y x y A}
41, 3eqtri 2373 1 x V A = {y x y A}
 Colors of variables: wff setvar class Syntax hints:  ∀wal 1540   = wceq 1642   ∈ wcel 1710  {cab 2339  ∀wral 2614  Vcvv 2859  ∩ciin 3970 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-ral 2619  df-v 2861  df-iin 3972 This theorem is referenced by: (None)
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