Theorem onssno 28233

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

Step	Hyp	Ref	Expression
1		df-ons 28231	. 2 ⊢ Ons = {𝑥 ∈ No ∣ ( R ‘𝑥) = ∅}
2		ssrab2 4031	. 2 ⊢ {𝑥 ∈ No ∣ ( R ‘𝑥) = ∅} ⊆ No
3	1, 2	eqsstri 3979	1 ⊢ Ons ⊆ No

Syntax hints:   = wceq 1542  {crab 3398   ⊆ wss 3900  ∅c0 4284  ‘cfv 6491   No csur 27609   R cright 27822  On_scons 28230

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1782  df-sb 2069  df-clab 2714  df-cleq 2727  df-clel 2810  df-rab 3399  df-ss 3917  df-ons 28231

This theorem is referenced by:  onsno  28234  onscutlt  28243  onsiso  28250  bdayon  28255  onsfi  28334