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Theorem elint2 3814
 Description: Membership in class intersection. (Contributed by NM, 14-Oct-1999.)
Hypothesis
Ref Expression
elint2.1
Assertion
Ref Expression
elint2
Distinct variable groups:   ,   ,

Proof of Theorem elint2
StepHypRef Expression
1 elint2.1 . . 3
21elint 3813 . 2
3 df-ral 2440 . 2
42, 3bitr4i 186 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wal 1333   wcel 2128  wral 2435  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-v 2714  df-int 3808 This theorem is referenced by:  elintg  3815  ssint  3823  intssunim  3829  iinuniss  3931  trint  4077  suplocexprlemmu  7632  suplocexprlemdisj  7634  suplocexprlemloc  7635  suplocexprlemub  7637
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