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Theorem nlim0 4131
 Description: The empty set is not a limit ordinal. (Contributed by NM, 24-Mar-1995.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
nlim0

Proof of Theorem nlim0
StepHypRef Expression
1 noel 3228 . . 3
2 simp2 905 . . 3
31, 2mto 588 . 2
4 dflim2 4107 . 2
53, 4mtbir 596 1
 Colors of variables: wff set class Syntax hints:   wn 3   w3a 885   wceq 1243   wcel 1393  c0 3224  cuni 3580   word 4099   wlim 4101 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-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-dif 2920  df-nul 3225  df-ilim 4106 This theorem is referenced by: (None)
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