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| Description: A surreal ordinal is a surreal. (Contributed by Scott Fenton, 18-Mar-2025.) | 
| Ref | Expression | 
|---|---|
| onsno | ⊢ (𝐴 ∈ Ons → 𝐴 ∈ No ) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | onssno 28278 | . 2 ⊢ Ons ⊆ No | |
| 2 | 1 | sseli 3978 | 1 ⊢ (𝐴 ∈ Ons → 𝐴 ∈ 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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