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Theorem inrab 3243
 Description: Intersection of two restricted class abstractions. (Contributed by NM, 1-Sep-2006.)
Assertion
Ref Expression
inrab

Proof of Theorem inrab
StepHypRef Expression
1 df-rab 2358 . . 3
2 df-rab 2358 . . 3
31, 2ineq12i 3172 . 2
4 df-rab 2358 . . 3
5 inab 3239 . . . 4
6 anandi 555 . . . . 5
76abbii 2195 . . . 4
85, 7eqtr4i 2105 . . 3
94, 8eqtr4i 2105 . 2
103, 9eqtr4i 2105 1
 Colors of variables: wff set class Syntax hints:   wa 102   wceq 1285   wcel 1434  cab 2068  crab 2353   cin 2973 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 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rab 2358  df-v 2604  df-in 2980 This theorem is referenced by:  rabnc  3284  unennn  10708
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