![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
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 28290 | . 2 ⊢ Ons = {𝑥 ∈ No ∣ ( R ‘𝑥) = ∅} | |
2 | ssrab2 4090 | . 2 ⊢ {𝑥 ∈ No ∣ ( R ‘𝑥) = ∅} ⊆ No | |
3 | 1, 2 | eqsstri 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 |
Copyright terms: Public domain | W3C validator |