Theorem onssno 28191

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 28189	. 2 ⊢ Ons = {𝑥 ∈ No ∣ ( R ‘𝑥) = ∅}
2		ssrab2 4027	. 2 ⊢ {𝑥 ∈ No ∣ ( R ‘𝑥) = ∅} ⊆ No
3	1, 2	eqsstri 3976	1 ⊢ Ons ⊆ No

Syntax hints:   = wceq 1541  {crab 3395   ⊆ wss 3897  ∅c0 4280  ‘cfv 6481   No csur 27578   R cright 27787  On_scons 28188

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-rab 3396  df-ss 3914  df-ons 28189

This theorem is referenced by:  onsno  28192  onscutlt  28201  onsiso  28205  bdayon  28209  onsfi  28283