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Theorem elon2 4160
 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 4159 . . 3
2 elex 2619 . . 3
31, 2jca 300 . 2
4 elong 4157 . . 3
54biimparc 293 . 2
63, 5impbii 124 1
 Colors of variables: wff set class Syntax hints:   wa 102   wb 103   wcel 1434  cvv 2610   word 4146  con0 4147 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-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-rex 2359  df-v 2612  df-in 2989  df-ss 2996  df-uni 3623  df-tr 3897  df-iord 4150  df-on 4152 This theorem is referenced by:  tfrexlem  6004
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