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Theorem onsno 28279
Description: A surreal ordinal is a surreal. (Contributed by Scott Fenton, 18-Mar-2025.)
Assertion
Ref Expression
onsno (𝐴 ∈ Ons𝐴 No )

Proof of Theorem onsno
StepHypRef Expression
1 onssno 28278 . 2 Ons No
21sseli 3978 1 (𝐴 ∈ Ons𝐴 No )
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2107   No csur 27685  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:  elons2  28282  sltonold  28284  onscutleft  28286  onaddscl  28287  onmulscl  28288
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