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Theorem ordnbtwn 4483
 Description: There is no set between an ordinal class and its successor. Generalized Proposition 7.25 of [TakeutiZaring] p. 41. (Contributed by NM, 21-Jun-1998.)
Assertion
Ref Expression
ordnbtwn

Proof of Theorem ordnbtwn
StepHypRef Expression
1 ordn2lp 4412 . . 3
2 ordirr 4410 . . 3
3 ioran 476 . . 3
41, 2, 3sylanbrc 645 . 2
5 elsuci 4458 . . . . 5
65anim2i 552 . . . 4
7 andi 837 . . . 4
86, 7sylib 188 . . 3
9 eleq2 2344 . . . . 5
109biimpac 472 . . . 4
1110orim2i 504 . . 3
128, 11syl 15 . 2
134, 12nsyl 113 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wo 357   wa 358   wceq 1623   wcel 1684   word 4391   csuc 4394 This theorem is referenced by:  onnbtwn  4484  ordsucss  4609 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-sbc 2992  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-opab 4078  df-tr 4114  df-eprel 4305  df-fr 4352  df-we 4354  df-ord 4395  df-suc 4398
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