Theorem onssno 28349

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 28347	. 2 ⊢ Ons = {𝑥 ∈ No ∣ ( R ‘𝑥) = ∅}
2		ssrab2 4035	. 2 ⊢ {𝑥 ∈ No ∣ ( R ‘𝑥) = ∅} ⊆ No
3	1, 2	eqsstri 3984	1 ⊢ Ons ⊆ No

Syntax hints:   = wceq 1562  {crab 3416   ⊆ wss 3906  ∅c0 4287  ‘cfv 6523   No csur 27706   R cright 27921  On_scons 28346

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1817  ax-4 1831  ax-5 1932  ax-6 1989  ax-7 2030  ax-8 2146  ax-9 2154  ax-ext 2736

This theorem depends on definitions:  df-bi 209  df-an 400  df-ex 1802  df-sb 2093  df-clab 2743  df-cleq 2756  df-clel 2839  df-rab 3417  df-ss 3923  df-ons 28347

This theorem is referenced by:  onno  28350  oncutlt  28359  oniso  28366  bdayons  28371  onsfi  28451