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Theorem 2on 6449
Description: Ordinal 2 is an ordinal number. (Contributed by NM, 18-Feb-2004.) (Proof shortened by Andrew Salmon, 12-Aug-2011.)
Assertion
Ref Expression
2on 2o ∈ On

Proof of Theorem 2on
StepHypRef Expression
1 df-2o 6441 . 2 2o = suc 1o
2 1on 6447 . . 3 1o ∈ On
32onsuci 4533 . 2 suc 1o ∈ On
41, 3eqeltri 2262 1 2o ∈ On
Colors of variables: wff set class
Syntax hints:  wcel 2160  Oncon0 4381  suc csuc 4383  1oc1o 6433  2oc2o 6434
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-13 2162  ax-14 2163  ax-ext 2171  ax-sep 4136  ax-nul 4144  ax-pow 4192  ax-pr 4227  ax-un 4451
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ral 2473  df-rex 2474  df-v 2754  df-dif 3146  df-un 3148  df-in 3150  df-ss 3157  df-nul 3438  df-pw 3592  df-sn 3613  df-pr 3614  df-uni 3825  df-tr 4117  df-iord 4384  df-on 4386  df-suc 4389  df-1o 6440  df-2o 6441
This theorem is referenced by:  3on  6451  infnninf  7151  onntri35  7265  bj-charfunbi  15016
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