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Theorem iinab 4391
 Description: Indexed intersection of a class builder. (Contributed by NM, 6-Dec-2011.)
Assertion
Ref Expression
iinab
Distinct variable groups:   ,   ,

Proof of Theorem iinab
StepHypRef Expression
1 nfcv 2619 . . . 4
2 nfab1 2621 . . . 4
31, 2nfiin 4359 . . 3
4 nfab1 2621 . . 3
53, 4cleqf 2646 . 2
6 abid 2444 . . . 4
76ralbii 2888 . . 3
8 vex 3112 . . . 4
9 eliin 4336 . . . 4
108, 9ax-mp 5 . . 3
11 abid 2444 . . 3
127, 10, 113bitr4i 277 . 2
135, 12mpgbir 1622 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  =wceq 1395  e.wcel 1818  {cab 2442  A.wral 2807   cvv 3109  |^|_ciin 4331 This theorem is referenced by:  iinrab  4392 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-v 3111  df-iin 4333
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