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Theorem iinrab 4155
 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 3725 . . 3
21abbidv 2552 . 2
3 df-rab 2716 . . . . 5
43a1i 11 . . . 4
54iineq2i 4114 . . 3
6 iinab 4154 . . 3
75, 6eqtri 2458 . 2
8 df-rab 2716 . 2
92, 7, 83eqtr4g 2495 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726  cab 2424   wne 2601  wral 2707  crab 2711  c0 3630  ciin 4096 This theorem is referenced by:  iinrab2  4156  riinrab  4169  ubthlem1  22377  pmapglbx  30639 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 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 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 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rab 2716  df-v 2960  df-dif 3325  df-nul 3631  df-iin 4098
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