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| Mirrors > Home > MPE Home > Th. List > onssno | Structured version Visualization version GIF version | ||
| Description: The surreal ordinals are a subclass of the surreals. (Contributed by Scott Fenton, 18-Mar-2025.) | 
| Ref | Expression | 
|---|---|
| onssno | ⊢ Ons ⊆ No | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | df-ons 28276 | . 2 ⊢ Ons = {𝑥 ∈ No ∣ ( R ‘𝑥) = ∅} | |
| 2 | ssrab2 4079 | . 2 ⊢ {𝑥 ∈ No ∣ ( R ‘𝑥) = ∅} ⊆ No | |
| 3 | 1, 2 | eqsstri 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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