Theorem onssno 28295

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 28293	. 2 ⊢ Ons = {𝑥 ∈ No ∣ ( R ‘𝑥) = ∅}
2		ssrab2 4103	. 2 ⊢ {𝑥 ∈ No ∣ ( R ‘𝑥) = ∅} ⊆ No
3	1, 2	eqsstri 4043	1 ⊢ Ons ⊆ No

Syntax hints:   = wceq 1537  {crab 3443   ⊆ wss 3976  ∅c0 4352  ‘cfv 6573   No csur 27702   R cright 27903  On_scons 28292

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-rab 3444  df-ss 3993  df-ons 28293

This theorem is referenced by:  onsno  28296