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Theorem iineq2 4348
 Description: Equality theorem for indexed intersection. (Contributed by NM, 22-Oct-2003.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
iineq2

Proof of Theorem iineq2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq2 2530 . . . . 5
21ralimi 2850 . . . 4
3 ralbi 2988 . . . 4
42, 3syl 16 . . 3
54abbidv 2593 . 2
6 df-iin 4333 . 2
7 df-iin 4333 . 2
85, 6, 73eqtr4g 2523 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  e.wcel 1818  {cab 2442  A.wral 2807  |^|_ciin 4331 This theorem is referenced by:  iineq2i  4350  iineq2d  4351  firest  14830  iincld  19540  elrfirn2  30628 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-iin 4333
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