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Theorem inrab2 3614
 Description: Intersection with a restricted class abstraction. (Contributed by NM, 19-Nov-2007.)
Assertion
Ref Expression
inrab2
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem inrab2
StepHypRef Expression
1 df-rab 2714 . . 3
2 abid2 2553 . . . 4
32eqcomi 2440 . . 3
41, 3ineq12i 3540 . 2
5 df-rab 2714 . . 3
6 inab 3609 . . . 4
7 elin 3530 . . . . . . 7
87anbi1i 677 . . . . . 6
9 an32 774 . . . . . 6
108, 9bitri 241 . . . . 5
1110abbii 2548 . . . 4
126, 11eqtr4i 2459 . . 3
135, 12eqtr4i 2459 . 2
144, 13eqtr4i 2459 1
 Colors of variables: wff set class Syntax hints:   wa 359   wceq 1652   wcel 1725  cab 2422  crab 2709   cin 3319 This theorem is referenced by:  iooval2  10949  fzval2  11046  smuval2  12994  smueqlem  13002  dfphi2  13163  ordtrest  17266  ordtrest2lem  17267  itg2addnclem2  26257 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-rab 2714  df-v 2958  df-in 3327
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