Theorem onsno 28279

Description: A surreal ordinal is a surreal. (Contributed by Scott Fenton, 18-Mar-2025.)

Assertion

Ref	Expression
onsno	⊢ (𝐴 ∈ Ons → 𝐴 ∈ No )

Proof of Theorem onsno

Step	Hyp	Ref	Expression
1		onssno 28278	. 2 ⊢ Ons ⊆ No
2	1	sseli 3978	1 ⊢ (𝐴 ∈ Ons → 𝐴 ∈ No )

Syntax hints:   → wi 4   ∈ wcel 2107   No csur 27685  On_scons 28275

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-rab 3436  df-ss 3967  df-ons 28276

This theorem is referenced by:  elons2  28282  sltonold  28284  onscutleft  28286  onaddscl  28287  onmulscl  28288