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Theorem iinrab 4145
Description: Indexed intersection of a restricted class builder. (Contributed by NM, 6-Dec-2011.)
Assertion
Ref Expression
iinrab
Distinct variable groups:   , ,   ,
Allowed substitution hints:   ( , )   ( )

Proof of Theorem iinrab
StepHypRef Expression
1 r19.28zv 3715 . . 3
21abbidv 2549 . 2
3 df-rab 2706 . . . . 5
43a1i 11 . . . 4
54iineq2i 4104 . . 3
6 iinab 4144 . . 3
75, 6eqtri 2455 . 2
8 df-rab 2706 . 2
92, 7, 83eqtr4g 2492 1
Colors of variables: wff set class
Syntax hints:  ->wi 4  /\wa 359  =wceq 1652  e.wcel 1725  {cab 2421  =/=wne 2598  A.wral 2697  {crab 2701   c0 3620  |^|_ciin 4086
This theorem is referenced by:  iinrab2  4146  riinrab  4158  ubthlem1  22364  pmapglbx  30503
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-or 360  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-nfc 2560  df-ne 2600  df-ral 2702  df-rab 2706  df-v 2950  df-dif 3315  df-nul 3621  df-iin 4088
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