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Theorem elon2 4305
 Description: An ordinal number is an ordinal set. (Contributed by NM, 8-Feb-2004.)
Assertion
Ref Expression
elon2

Proof of Theorem elon2
StepHypRef Expression
1 eloni 4304 . . 3
2 elex 2700 . . 3
31, 2jca 304 . 2
4 elong 4302 . . 3
54biimparc 297 . 2
63, 5impbii 125 1
 Colors of variables: wff set class Syntax hints:   wa 103   wb 104   wcel 1481  cvv 2689   word 4291  con0 4292 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-rex 2423  df-v 2691  df-in 3081  df-ss 3088  df-uni 3744  df-tr 4034  df-iord 4295  df-on 4297 This theorem is referenced by:  tfrexlem  6238
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