Theorem onssno 28640

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 28638	. 2 ⊢ Ons = {𝑥 ∈ No ∣ (R‘𝑥) = ∅}
2		ssrab2 4005	. 2 ⊢ {𝑥 ∈ No ∣ (R‘𝑥) = ∅} ⊆ No
3	1, 2	eqsstri 3954	1 ⊢ Ons ⊆ No

This proof depends on syntax axioms:   = wceq 1569  {crab 3412   ⊆ wss 3895  ∅c0 4278  ‘cfv 6538  Nocsur 27997  Rcright 28212  On_scons 28637

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-rab 3413  df-ss 3896  df-ons 28638

This theorem is used by:  onno  28641  oncutlt  28650  oniso  28657  bdayons  28662  onsfi  28742