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Theorem iinab 4360
 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 2580 . . . 4
2 nfab1 2582 . . . 4
31, 2nfiin 4328 . . 3
4 nfab1 2582 . . 3
53, 4cleqf 2607 . 2
6 abid 2409 . . . 4
76ralbii 2853 . . 3
8 vex 3083 . . . 4
9 eliin 4305 . . . 4
108, 9ax-mp 5 . . 3
11 abid 2409 . . 3
127, 10, 113bitr4i 280 . 2
135, 12mpgbir 1667 1
 Colors of variables: wff setvar class Syntax hints:   wb 187   wceq 1437   wcel 1872  cab 2407  wral 2771  cvv 3080  ciin 4300 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ral 2776  df-v 3082  df-iin 4302 This theorem is referenced by:  iinrab  4361
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