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Theorem 2on 6040
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  e.  On

Proof of Theorem 2on
StepHypRef Expression
1 df-2o 6033 . 2  |-  2o  =  suc  1o
2 1on 6039 . . 3  |-  1o  e.  On
32onsuci 4270 . 2  |-  suc  1o  e.  On
41, 3eqeltri 2126 1  |-  2o  e.  On
Colors of variables: wff set class
Syntax hints:    e. wcel 1409   Oncon0 4128   suc csuc 4130   1oc1o 6025   2oc2o 6026
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-13 1420  ax-14 1421  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-sep 3903  ax-nul 3911  ax-pow 3955  ax-pr 3972  ax-un 4198
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-rex 2329  df-v 2576  df-dif 2948  df-un 2950  df-in 2952  df-ss 2959  df-nul 3253  df-pw 3389  df-sn 3409  df-pr 3410  df-uni 3609  df-tr 3883  df-iord 4131  df-on 4133  df-suc 4136  df-1o 6032  df-2o 6033
This theorem is referenced by:  3on  6042
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