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Theorem 2on 6404
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 6396 . 2 2o = suc 1o
2 1on 6402 . . 3 1o ∈ On
32onsuci 4500 . 2 suc 1o ∈ On
41, 3eqeltri 2243 1 2o ∈ On
Colors of variables: wff set class
Syntax hints:  wcel 2141  Oncon0 4348  suc csuc 4350  1oc1o 6388  2oc2o 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 4107  ax-nul 4115  ax-pow 4160  ax-pr 4194  ax-un 4418
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 3568  df-sn 3589  df-pr 3590  df-uni 3797  df-tr 4088  df-iord 4351  df-on 4353  df-suc 4356  df-1o 6395  df-2o 6396
This theorem is referenced by:  3on  6406  infnninf  7100  onntri35  7214  bj-charfunbi  13846
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