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Theorem eloni 4061
Description: An ordinal number has the ordinal property. (Contributed by NM, 5-Jun-1994.)
Assertion
Ref Expression
eloni (A On → Ord A)

Proof of Theorem eloni
StepHypRef Expression
1 elong 4059 . 2 (A On → (A On ↔ Ord A))
21ibi 165 1 (A On → Ord A)
Colors of variables: wff set class
Syntax hints:  wi 4   wcel 1374  Ord word 4048  Oncon0 4049
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-ral 2289  df-rex 2290  df-v 2537  df-in 2901  df-ss 2908  df-uni 3555  df-tr 3829  df-iord 4052  df-on 4054
This theorem is referenced by:  elon2  4062  onelon  4070  onin  4072  onelss  4073  ontr1  4075  onordi  4113  onss  4169  suceloni  4177  sucelon  4179  onsucmin  4182  onsucelsucr  4183  ordsucunielexmid  4200  nnord  4261  tfrlem1  5845  tfrlemisucaccv  5860  tfrlemibfn  5863  tfrlemiubacc  5865  tfrexlem  5870  sucinc2  5941
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