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Theorem iineq2 3674
 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 2101 . . . . 5
21ralimi 2384 . . . 4
3 ralbi 2445 . . . 4
42, 3syl 14 . . 3
54abbidv 2155 . 2
6 df-iin 3660 . 2
7 df-iin 3660 . 2
85, 6, 73eqtr4g 2097 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wceq 1243   wcel 1393  cab 2026  wral 2306  ciin 3658 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-ral 2311  df-iin 3660 This theorem is referenced by:  iineq2i  3676  iineq2d  3677
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