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Theorem 2on 6274
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 6266 . 2 2o = suc 1o
2 1on 6272 . . 3 1o ∈ On
32onsuci 4390 . 2 suc 1o ∈ On
41, 3eqeltri 2185 1 2o ∈ On
Colors of variables: wff set class
Syntax hints:  wcel 1461  Oncon0 4243  suc csuc 4245  1oc1o 6258  2oc2o 6259
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-io 681  ax-5 1404  ax-7 1405  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-8 1463  ax-10 1464  ax-11 1465  ax-i12 1466  ax-bndl 1467  ax-4 1468  ax-13 1472  ax-14 1473  ax-17 1487  ax-i9 1491  ax-ial 1495  ax-i5r 1496  ax-ext 2095  ax-sep 4004  ax-nul 4012  ax-pow 4056  ax-pr 4089  ax-un 4313
This theorem depends on definitions:  df-bi 116  df-tru 1315  df-nf 1418  df-sb 1717  df-clab 2100  df-cleq 2106  df-clel 2109  df-nfc 2242  df-ral 2393  df-rex 2394  df-v 2657  df-dif 3037  df-un 3039  df-in 3041  df-ss 3048  df-nul 3328  df-pw 3476  df-sn 3497  df-pr 3498  df-uni 3701  df-tr 3985  df-iord 4246  df-on 4248  df-suc 4251  df-1o 6265  df-2o 6266
This theorem is referenced by:  3on  6276
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