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Theorem 4on 6076
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 6068 . 2 4𝑜 = suc 3𝑜
2 3on 6075 . . 3 3𝑜 ∈ On
32onsuci 4268 . 2 suc 3𝑜 ∈ On
41, 3eqeltri 2152 1 4𝑜 ∈ On
Colors of variables: wff set class
Syntax hints:  wcel 1434  Oncon0 4126  suc csuc 4128  3𝑜c3o 6060  4𝑜c4o 6061
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-in1 577  ax-in2 578  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-13 1445  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-nul 3912  ax-pow 3956  ax-pr 3972  ax-un 4196
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-v 2604  df-dif 2976  df-un 2978  df-in 2980  df-ss 2987  df-nul 3259  df-pw 3392  df-sn 3412  df-pr 3413  df-uni 3610  df-tr 3884  df-iord 4129  df-on 4131  df-suc 4134  df-1o 6065  df-2o 6066  df-3o 6067  df-4o 6068
This theorem is referenced by: (None)
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