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Theorem 3on 8479
Description: Ordinal 3 is an ordinal number. (Contributed by Mario Carneiro, 5-Jan-2016.)
Assertion
Ref Expression
3on 3o ∈ On

Proof of Theorem 3on
StepHypRef Expression
1 df-3o 8463 . 2 3o = suc 2o
2 2on 8475 . . 3 2o ∈ On
32onsuci 7820 . 2 suc 2o ∈ On
41, 3eqeltri 2821 1 3o ∈ On
Colors of variables: wff setvar class
Syntax hints:  wcel 2098  Oncon0 6354  suc csuc 6356  2oc2o 8455  3oc3o 8456
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695  ax-sep 5289  ax-nul 5296  ax-pr 5417  ax-un 7718
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3or 1085  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-ne 2933  df-ral 3054  df-rex 3063  df-rab 3425  df-v 3468  df-dif 3943  df-un 3945  df-in 3947  df-ss 3957  df-pss 3959  df-nul 4315  df-if 4521  df-pw 4596  df-sn 4621  df-pr 4623  df-op 4627  df-uni 4900  df-br 5139  df-opab 5201  df-tr 5256  df-eprel 5570  df-po 5578  df-so 5579  df-fr 5621  df-we 5623  df-ord 6357  df-on 6358  df-suc 6360  df-1o 8461  df-2o 8462  df-3o 8463
This theorem is referenced by:  4on  8480  oenord1  42555  3no  42678  nlim4  42685  clsk1independent  43286
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