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Theorem 3on 8480
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 8464 . 2 3o = suc 2o
2 2on 8476 . . 3 2o ∈ On
32onsuci 7823 . 2 suc 2o ∈ On
41, 3eqeltri 2829 1 3o ∈ On
Colors of variables: wff setvar class
Syntax hints:  wcel 2106  Oncon0 6361  suc csuc 6363  2oc2o 8456  3oc3o 8457
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703  ax-sep 5298  ax-nul 5305  ax-pr 5426  ax-un 7721
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3or 1088  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-ne 2941  df-ral 3062  df-rex 3071  df-rab 3433  df-v 3476  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-pss 3966  df-nul 4322  df-if 4528  df-pw 4603  df-sn 4628  df-pr 4630  df-op 4634  df-uni 4908  df-br 5148  df-opab 5210  df-tr 5265  df-eprel 5579  df-po 5587  df-so 5588  df-fr 5630  df-we 5632  df-ord 6364  df-on 6365  df-suc 6367  df-1o 8462  df-2o 8463  df-3o 8464
This theorem is referenced by:  4on  8481  oenord1  42051  3no  42174  nlim4  42181  clsk1independent  42782
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