Theorem onssno 28667

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 28665	. 2 ⊢ Ons = {𝑥 ∈ No ∣ (R‘𝑥) = ∅}
2		ssrab2 4008	. 2 ⊢ {𝑥 ∈ No ∣ (R‘𝑥) = ∅} ⊆ No
3	1, 2	eqsstri 3959	1 ⊢ Ons ⊆ No

This proof depends on syntax axioms:   = wceq 1570  {crab 3416   ⊆ wss 3900  ∅c0 4281  ‘cfv 6555  Nocsur 28024  Rcright 28239  On_scons 28664

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-rab 3417  df-ss 3901  df-ons 28665

This theorem is used by:  onno  28668  oncutlt  28677  oniso  28684  bdayons  28689  onsfi  28769