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Theorem inrab2 3620
 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 2722 . . 3
2 abid2 2558 . . . 4
32eqcomi 2445 . . 3
41, 3ineq12i 3547 . 2
5 df-rab 2722 . . 3
6 inab 3615 . . . 4
7 elin 3536 . . . . . . 7
87anbi1i 690 . . . . . 6
9 an32 791 . . . . . 6
108, 9bitri 249 . . . . 5
1110abbii 2553 . . . 4
126, 11eqtr4i 2464 . . 3
135, 12eqtr4i 2464 . 2
144, 13eqtr4i 2464 1
 Colors of variables: wff setvar class Syntax hints:   wa 369   wceq 1364   wcel 1761  cab 2427  crab 2717   cin 3324 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1713  ax-7 1733  ax-10 1780  ax-11 1785  ax-12 1797  ax-13 1948  ax-ext 2422 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1367  df-ex 1592  df-nf 1595  df-sb 1706  df-clab 2428  df-cleq 2434  df-clel 2437  df-nfc 2566  df-rab 2722  df-v 2972  df-in 3332 This theorem is referenced by:  iooval2  11329  fzval2  11436  smuval2  13674  smueqlem  13682  dfphi2  13845  ordtrest  18765  ordtrest2lem  18766  ordtrestNEW  26287  ordtrest2NEWlem  26288  itg2addnclem2  28369
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