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Theorem 3on 8111
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 8101 . 2 3o = suc 2o
2 2on 8108 . . 3 2o ∈ On
32onsuci 7548 . 2 suc 2o ∈ On
41, 3eqeltri 2912 1 3o ∈ On
Colors of variables: wff setvar class
Syntax hints:  wcel 2115  Oncon0 6179  suc csuc 6181  2oc2o 8093  3oc3o 8094
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 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796  ax-sep 5190  ax-nul 5197  ax-pr 5318  ax-un 7456
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3or 1085  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-mo 2624  df-eu 2655  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-ne 3015  df-ral 3138  df-rex 3139  df-rab 3142  df-v 3483  df-sbc 3760  df-dif 3923  df-un 3925  df-in 3927  df-ss 3937  df-pss 3939  df-nul 4278  df-if 4452  df-pw 4525  df-sn 4552  df-pr 4554  df-tp 4556  df-op 4558  df-uni 4826  df-br 5054  df-opab 5116  df-tr 5160  df-eprel 5453  df-po 5462  df-so 5463  df-fr 5502  df-we 5504  df-ord 6182  df-on 6183  df-suc 6185  df-1o 8099  df-2o 8100  df-3o 8101
This theorem is referenced by:  4on  8112  clsk1independent  40669
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