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Theorem 4on 6405
Description: Ordinal 3 is an ordinal number. (Contributed by Mario Carneiro, 5-Jan-2016.)
Assertion
Ref Expression
4on  |-  4o  e.  On

Proof of Theorem 4on
StepHypRef Expression
1 df-4o 6396 . 2  |-  4o  =  suc  3o
2 3on 6404 . . 3  |-  3o  e.  On
32onsuci 4498 . 2  |-  suc  3o  e.  On
41, 3eqeltri 2243 1  |-  4o  e.  On
Colors of variables: wff set class
Syntax hints:    e. wcel 2141   Oncon0 4346   suc csuc 4348   3oc3o 6388   4oc4o 6389
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 609  ax-in2 610  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-13 2143  ax-14 2144  ax-ext 2152  ax-sep 4105  ax-nul 4113  ax-pow 4158  ax-pr 4192  ax-un 4416
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-ral 2453  df-rex 2454  df-v 2732  df-dif 3123  df-un 3125  df-in 3127  df-ss 3134  df-nul 3415  df-pw 3566  df-sn 3587  df-pr 3588  df-uni 3795  df-tr 4086  df-iord 4349  df-on 4351  df-suc 4354  df-1o 6393  df-2o 6394  df-3o 6395  df-4o 6396
This theorem is referenced by: (None)
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