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Theorem bj-dfom 13346
 Description: Alternate definition of , as the intersection of all the inductive sets. Proposal: make this the definition. (Contributed by BJ, 30-Nov-2019.)
Assertion
Ref Expression
bj-dfom Ind

Proof of Theorem bj-dfom
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfom3 4516 . 2
2 df-bj-ind 13340 . . . . 5 Ind
32bicomi 131 . . . 4 Ind
43abbii 2256 . . 3 Ind
54inteqi 3784 . 2 Ind
61, 5eqtri 2161 1 Ind
 Colors of variables: wff set class Syntax hints:   wa 103   wceq 1332   wcel 1481  cab 2126  wral 2417  c0 3369  cint 3780   csuc 4297  com 4514  Ind wind 13339 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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-int 3781  df-iom 4515  df-bj-ind 13340 This theorem is referenced by:  bj-omind  13347  bj-omssind  13348  bj-ssom  13349
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