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Theorem onss 4774
Description: An ordinal number is a subset of the class of ordinal numbers. (Contributed by NM, 5-Jun-1994.)
Assertion
Ref Expression
onss  |-  ( A  e.  On  ->  A  C_  On )

Proof of Theorem onss
StepHypRef Expression
1 eloni 4594 . 2  |-  ( A  e.  On  ->  Ord  A )
2 ordsson 4773 . 2  |-  ( Ord 
A  ->  A  C_  On )
31, 2syl 16 1  |-  ( A  e.  On  ->  A  C_  On )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1726    C_ wss 3322   Ord word 4583   Oncon0 4584
This theorem is referenced by:  onuni  4776  onminex  4790  suceloni  4796  onssi  4820  tfi  4836  tfr3  6663  tz7.49  6705  tz7.49c  6706  oacomf1olem  6810  oeeulem  6847  ordtypelem2  7491  cantnfcl  7625  cantnflt  7630  cantnfp1lem3  7639  oemapvali  7643  cantnflem1c  7646  cantnflem1d  7647  cantnflem1  7648  cantnf  7652  cnfcom  7660  cnfcom3lem  7663  infxpenlem  7900  ac10ct  7920  dfac12lem1  8028  dfac12lem2  8029  cfeq0  8141  cfsuc  8142  cff1  8143  cfflb  8144  cofsmo  8154  cfsmolem  8155  alephsing  8161  zorn2lem2  8382  ttukeylem3  8396  ttukeylem5  8398  ttukeylem6  8399  inar1  8655  predon  25473  soseq  25534  nobnddown  25661  nofulllem5  25666  ontgval  26186  aomclem6  27148
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406  ax-un 4704
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 938  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-pss 3338  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-tp 3824  df-op 3825  df-uni 4018  df-br 4216  df-opab 4270  df-tr 4306  df-eprel 4497  df-po 4506  df-so 4507  df-fr 4544  df-we 4546  df-ord 4587  df-on 4588
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