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Theorem onss 4734
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 4555 . 2  |-  ( A  e.  On  ->  Ord  A )
2 ordsson 4733 . 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 1721    C_ wss 3284   Ord word 4544   Oncon0 4545
This theorem is referenced by:  onuni  4736  onminex  4750  suceloni  4756  onssi  4780  tfi  4796  tfr3  6623  tz7.49  6665  tz7.49c  6666  oacomf1olem  6770  oeeulem  6807  ordtypelem2  7448  cantnfcl  7582  cantnflt  7587  cantnfp1lem3  7596  oemapvali  7600  cantnflem1c  7603  cantnflem1d  7604  cantnflem1  7605  cantnf  7609  cnfcom  7617  cnfcom3lem  7620  infxpenlem  7855  ac10ct  7875  dfac12lem1  7983  dfac12lem2  7984  cfeq0  8096  cfsuc  8097  cff1  8098  cfflb  8099  cofsmo  8109  cfsmolem  8110  alephsing  8116  zorn2lem2  8337  ttukeylem3  8351  ttukeylem5  8353  ttukeylem6  8354  inar1  8610  predon  25411  soseq  25472  nobnddown  25573  nofulllem5  25578  ontgval  26089  aomclem6  27028
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-13 1723  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389  ax-sep 4294  ax-nul 4302  ax-pr 4367  ax-un 4664
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2262  df-mo 2263  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-ne 2573  df-ral 2675  df-rex 2676  df-rab 2679  df-v 2922  df-sbc 3126  df-dif 3287  df-un 3289  df-in 3291  df-ss 3298  df-pss 3300  df-nul 3593  df-if 3704  df-sn 3784  df-pr 3785  df-tp 3786  df-op 3787  df-uni 3980  df-br 4177  df-opab 4231  df-tr 4267  df-eprel 4458  df-po 4467  df-so 4468  df-fr 4505  df-we 4507  df-ord 4548  df-on 4549
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