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Theorem onnbtwn 4927
Description: There is no set between an ordinal number and its successor. Proposition 7.25 of [TakeutiZaring] p. 41. (Contributed by NM, 9-Jun-1994.)
Assertion
Ref Expression
onnbtwn

Proof of Theorem onnbtwn
StepHypRef Expression
1 eloni 4846 . 2
2 ordnbtwn 4926 . 2
31, 2syl 16 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369  e.wcel 1758  Ordword 4835   con0 4836  succsuc 4838
This theorem is referenced by:  ordunisuc2  6588  oalimcl  7133  omlimcl  7151  oneo  7154  nnneo  7224
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4530  ax-nul 4538  ax-pr 4648
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2266  df-mo 2267  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2805  df-rex 2806  df-rab 2809  df-v 3083  df-sbc 3298  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3752  df-if 3906  df-sn 3994  df-pr 3996  df-op 4000  df-uni 4209  df-br 4410  df-opab 4468  df-tr 4503  df-eprel 4749  df-po 4758  df-so 4759  df-fr 4796  df-we 4798  df-ord 4839  df-on 4840  df-suc 4842
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