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Theorem iineq2 4287
 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 2538 . . . . 5
21ralimi 2796 . . . 4
3 ralbi 2908 . . . 4
42, 3syl 17 . . 3
54abbidv 2589 . 2
6 df-iin 4272 . 2
7 df-iin 4272 . 2
85, 6, 73eqtr4g 2530 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wceq 1452   wcel 1904  cab 2457  wral 2756  ciin 4270 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-ral 2761  df-iin 4272 This theorem is referenced by:  iineq2i  4289  iineq2d  4290  firest  15409  iincld  20131  elrfirn2  35609
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