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Theorem elintrab 3819
 Description: Membership in the intersection of a class abstraction. (Contributed by NM, 17-Oct-1999.)
Hypothesis
Ref Expression
inteqab.1
Assertion
Ref Expression
elintrab
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem elintrab
StepHypRef Expression
1 inteqab.1 . . . 4
21elintab 3818 . . 3
3 impexp 261 . . . 4
43albii 1450 . . 3
52, 4bitri 183 . 2
6 df-rab 2444 . . . 4
76inteqi 3811 . . 3
87eleq2i 2224 . 2
9 df-ral 2440 . 2
105, 8, 93bitr4i 211 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1333   wcel 2128  cab 2143  wral 2435  crab 2439  cvv 2712  cint 3807 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ral 2440  df-rab 2444  df-v 2714  df-int 3808 This theorem is referenced by:  elintrabg  3820  intmin  3827  bj-indint  13466
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