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Theorem iinab 4152
 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 2572 . . . 4
2 nfab1 2574 . . . 4
31, 2nfiin 4120 . . 3
4 nfab1 2574 . . 3
53, 4cleqf 2596 . 2
6 abid 2424 . . . 4
76ralbii 2729 . . 3
8 vex 2959 . . . 4
9 eliin 4098 . . . 4
108, 9ax-mp 8 . . 3
11 abid 2424 . . 3
127, 10, 113bitr4i 269 . 2
135, 12mpgbir 1559 1
 Colors of variables: wff set class Syntax hints:   wb 177   wceq 1652   wcel 1725  cab 2422  wral 2705  cvv 2956  ciin 4094 This theorem is referenced by:  iinrab  4153 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-v 2958  df-iin 4096
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