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Theorem onelss 4925
Description: An element of an ordinal number is a subset of the number. (Contributed by NM, 5-Jun-1994.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
onelss

Proof of Theorem onelss
StepHypRef Expression
1 eloni 4893 . 2
2 ordelss 4899 . . 3
32ex 434 . 2
41, 3syl 16 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  e.wcel 1818  C_wss 3475  Ordword 4882   con0 4883
This theorem is referenced by:  ordunidif  4931  onelssi  4991  ssorduni  6621  suceloni  6648  tfisi  6693  tfrlem9  7073  tfrlem11  7076  oaordex  7226  oaass  7229  odi  7247  omass  7248  oewordri  7260  nnaordex  7306  domtriord  7683  hartogs  7990  card2on  8001  tskwe  8352  infxpenlem  8412  cfub  8650  cfsuc  8658  coflim  8662  hsmexlem2  8828  ondomon  8959  pwcfsdom  8979  inar1  9174  tskord  9179  grudomon  9216  gruina  9217  dfrdg2  29228  poseq  29333  sltres  29424  nobndup  29460  nobnddown  29461  aomclem6  31005
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111  df-in 3482  df-ss 3489  df-uni 4250  df-tr 4546  df-po 4805  df-so 4806  df-fr 4843  df-we 4845  df-ord 4886  df-on 4887
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