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Theorem iinab 3718
 Description: Indexed intersection of a class builder. (Contributed by NM, 6-Dec-2011.)
Assertion
Ref Expression
iinab
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem iinab
StepHypRef Expression
1 nfcv 2178 . . . 4
2 nfab1 2180 . . . 4
31, 2nfiinxy 3684 . . 3
4 nfab1 2180 . . 3
53, 4cleqf 2201 . 2
6 abid 2028 . . . 4
76ralbii 2330 . . 3
8 vex 2560 . . . 4
9 eliin 3662 . . . 4
108, 9ax-mp 7 . . 3
11 abid 2028 . . 3
127, 10, 113bitr4i 201 . 2
135, 12mpgbir 1342 1
 Colors of variables: wff set class Syntax hints:   wb 98   wceq 1243   wcel 1393  cab 2026  wral 2306  cvv 2557  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-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  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-nfc 2167  df-ral 2311  df-v 2559  df-iin 3660 This theorem is referenced by:  iinrabm  3719
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