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Theorem iineq2 4102
 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 2496 . . . . 5
21ralimi 2773 . . . 4
3 ralbi 2834 . . . 4
42, 3syl 16 . . 3
54abbidv 2549 . 2
6 df-iin 4088 . 2
7 df-iin 4088 . 2
85, 6, 73eqtr4g 2492 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652   wcel 1725  cab 2421  wral 2697  ciin 4086 This theorem is referenced by:  iineq2i  4104  iineq2d  4105  firest  13652  iincld  17095  elrfirn2  26741 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-ral 2702  df-iin 4088
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