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Theorem 4on 6293
Description: Ordinal 3 is an ordinal number. (Contributed by Mario Carneiro, 5-Jan-2016.)
Assertion
Ref Expression
4on 4o ∈ On

Proof of Theorem 4on
StepHypRef Expression
1 df-4o 6284 . 2 4o = suc 3o
2 3on 6292 . . 3 3o ∈ On
32onsuci 4402 . 2 suc 3o ∈ On
41, 3eqeltri 2190 1 4o ∈ On
Colors of variables: wff set class
Syntax hints:  wcel 1465  Oncon0 4255  suc csuc 4257  3oc3o 6276  4oc4o 6277
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-in1 588  ax-in2 589  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-13 1476  ax-14 1477  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-sep 4016  ax-nul 4024  ax-pow 4068  ax-pr 4101  ax-un 4325
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-ral 2398  df-rex 2399  df-v 2662  df-dif 3043  df-un 3045  df-in 3047  df-ss 3054  df-nul 3334  df-pw 3482  df-sn 3503  df-pr 3504  df-uni 3707  df-tr 3997  df-iord 4258  df-on 4260  df-suc 4263  df-1o 6281  df-2o 6282  df-3o 6283  df-4o 6284
This theorem is referenced by: (None)
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