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Theorem onssno 28292
Description: The surreal ordinals are a subclass of the surreals. (Contributed by Scott Fenton, 18-Mar-2025.)
Assertion
Ref Expression
onssno Ons No

Proof of Theorem onssno
StepHypRef Expression
1 df-ons 28290 . 2 Ons = {𝑥 No ∣ ( R ‘𝑥) = ∅}
2 ssrab2 4090 . 2 {𝑥 No ∣ ( R ‘𝑥) = ∅} ⊆ No
31, 2eqsstri 4030 1 Ons No
Colors of variables: wff setvar class
Syntax hints:   = wceq 1537  {crab 3433  wss 3963  c0 4339  cfv 6563   No csur 27699   R cright 27900  Onscons 28289
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-rab 3434  df-ss 3980  df-ons 28290
This theorem is referenced by:  onsno  28293
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