Theorem onsno 28296

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 28295	. 2 ⊢ Ons ⊆ No
2	1	sseli 4004	1 ⊢ (𝐴 ∈ Ons → 𝐴 ∈ No )

Syntax hints:   → wi 4   ∈ wcel 2108   No csur 27702  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:  elons2  28299  sltonold  28301  onscutleft  28303  onaddscl  28304  onmulscl  28305