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Theorem iinrab 4183
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 3749 . . 3
21abbidv 2557 . 2
3 df-rab 2721 . . . . 5
43a1i 11 . . . 4
54iineq2i 4141 . . 3
6 iinab 4182 . . 3
75, 6eqtri 2463 . 2
8 df-rab 2721 . 2
92, 7, 83eqtr4g 2500 1
Colors of variables: wff set class
Syntax hints:  ->wi 4  /\wa 360  =wceq 1654  e.wcel 1728  {cab 2429  =/=wne 2606  A.wral 2712  {crab 2716   c0 3616  |^|_ciin 4123
This theorem is referenced by:  iinrab2  4184  riinrab  4197  ubthlem1  22423  pmapglbx  30806
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ne 2608  df-ral 2717  df-rab 2721  df-v 2967  df-dif 3312  df-nul 3617  df-iin 4125
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