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Theorem onelpss 4613
 Description: Relationship between membership and proper subset of an ordinal number. (Contributed by NM, 15-Sep-1995.)
Assertion
Ref Expression
onelpss

Proof of Theorem onelpss
StepHypRef Expression
1 eloni 4583 . 2
2 eloni 4583 . 2
3 ordelssne 4600 . 2
41, 2, 3syl2an 464 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wcel 1725   wne 2598   wss 3312   word 4572  con0 4573 This theorem is referenced by:  tfindsg  4832  findsg  4864  oancom  7598  cardsdom2  7867  alephord  7948 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-tr 4295  df-eprel 4486  df-po 4495  df-so 4496  df-fr 4533  df-we 4535  df-ord 4576  df-on 4577
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