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Theorem inrab2 3253
 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 2362 . . 3
2 abid2 2203 . . . 4
32eqcomi 2087 . . 3
41, 3ineq12i 3181 . 2
5 df-rab 2362 . . 3
6 inab 3248 . . . 4
7 elin 3165 . . . . . . 7
87anbi1i 446 . . . . . 6
9 an32 527 . . . . . 6
108, 9bitri 182 . . . . 5
1110abbii 2198 . . . 4
126, 11eqtr4i 2106 . . 3
135, 12eqtr4i 2106 . 2
144, 13eqtr4i 2106 1
 Colors of variables: wff set class Syntax hints:   wa 102   wceq 1285   wcel 1434  cab 2069  crab 2357   cin 2981 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-rab 2362  df-v 2612  df-in 2988 This theorem is referenced by:  iooval2  9066  fzval2  9160  dfphi2  10803  znnen  10818
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