Theorem renod 28742

Description: A surreal real is a surreal number. (Contributed by Scott Fenton, 19-Feb-2026.)

Hypothesis

Ref	Expression
renod.1	⊢ (𝜑 → 𝐴 ∈ ℝs)

Assertion

Ref	Expression
renod	⊢ (𝜑 → 𝐴 ∈ No )

Proof of Theorem renod

Step	Hyp	Ref	Expression
1		renod.1	. 2 ⊢ (𝜑 → 𝐴 ∈ ℝs)
2		reno 28741	. 2 ⊢ (𝐴 ∈ ℝs → 𝐴 ∈ No )
3	1, 2	syl 18	1 ⊢ (𝜑 → 𝐴 ∈ No )

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2146   No csur 27860  ℝ_screno 28738

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 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-rex 3092  df-rab 3419  df-v 3459  df-dif 3909  df-un 3911  df-ss 3923  df-nul 4287  df-if 4490  df-sn 4592  df-pr 4594  df-op 4598  df-uni 4875  df-br 5112  df-iota 6497  df-fv 6549  df-ov 7423  df-reno 28739

This theorem is used by: (None)