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Theorem elin3 3173
 Description: Membership in a class defined as a ternary intersection. (Contributed by Stefan O'Rear, 29-Mar-2015.)
Hypothesis
Ref Expression
elin3.x
Assertion
Ref Expression
elin3

Proof of Theorem elin3
StepHypRef Expression
1 elin 3165 . . 3
21anbi1i 446 . 2
3 elin3.x . . 3
43elin2 3170 . 2
5 df-3an 922 . 2
62, 4, 53bitr4i 210 1
 Colors of variables: wff set class Syntax hints:   wa 102   wb 103   w3a 920   wceq 1285   wcel 1434   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-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-in 2988 This theorem is referenced by: (None)
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