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Theorem eloni 4078
Description: An ordinal number has the ordinal property. (Contributed by NM, 5-Jun-1994.)
Assertion
Ref Expression
eloni  On  Ord

Proof of Theorem eloni
StepHypRef Expression
1 elong 4076 . 2  On  On  Ord
21ibi 165 1  On  Ord
Colors of variables: wff set class
Syntax hints:   wi 4   wcel 1390   Ord word 4065   Oncon0 4066
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-in 2918  df-ss 2925  df-uni 3572  df-tr 3846  df-iord 4069  df-on 4071
This theorem is referenced by:  elon2  4079  onelon  4087  onin  4089  onelss  4090  ontr1  4092  onordi  4129  onss  4185  suceloni  4193  sucelon  4195  onsucmin  4198  onsucelsucr  4199  ordsucunielexmid  4216  nnord  4277  tfrlem1  5864  tfrlemisucaccv  5880  tfrlemibfn  5883  tfrlemiubacc  5885  tfrexlem  5889  sucinc2  5965
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