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Theorem onssno 28278
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 28276 . 2 Ons = {𝑥 No ∣ ( R ‘𝑥) = ∅}
2 ssrab2 4079 . 2 {𝑥 No ∣ ( R ‘𝑥) = ∅} ⊆ No
31, 2eqsstri 4029 1 Ons No
Colors of variables: wff setvar class
Syntax hints:   = wceq 1539  {crab 3435  wss 3950  c0 4332  cfv 6560   No csur 27685   R cright 27886  Onscons 28275
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-rab 3436  df-ss 3967  df-ons 28276
This theorem is referenced by:  onsno  28279
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