Theorem onssno 28155

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 28153	. 2 ⊢ Ons = {𝑥 ∈ No ∣ ( R ‘𝑥) = ∅}
2		ssrab2 4043	. 2 ⊢ {𝑥 ∈ No ∣ ( R ‘𝑥) = ∅} ⊆ No
3	1, 2	eqsstri 3993	1 ⊢ Ons ⊆ No

Syntax hints:   = wceq 1540  {crab 3405   ⊆ wss 3914  ∅c0 4296  ‘cfv 6511   No csur 27551   R cright 27754  On_scons 28152

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-rab 3406  df-ss 3931  df-ons 28153

This theorem is referenced by:  onsno  28156  onscutlt  28165  onsiso  28169  bdayon  28173  onsfi  28247