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Theorem iinrabm 3747
 Description: Indexed intersection of a restricted class builder. (Contributed by Jim Kingdon, 16-Aug-2018.)
Assertion
Ref Expression
iinrabm
Distinct variable groups:   ,,   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem iinrabm
StepHypRef Expression
1 r19.28mv 3342 . . 3
21abbidv 2171 . 2
3 df-rab 2332 . . . . 5
43a1i 9 . . . 4
54iineq2i 3704 . . 3
6 iinab 3746 . . 3
75, 6eqtri 2076 . 2
8 df-rab 2332 . 2
92, 7, 83eqtr4g 2113 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wceq 1259  wex 1397   wcel 1409  cab 2042  wral 2323  crab 2327  ciin 3686 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-rab 2332  df-v 2576  df-iin 3688 This theorem is referenced by: (None)
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