Theorem renod 28880

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 28879	. 2 ⊢ (𝐴 ∈ ℝs → 𝐴 ∈ No)
3	1, 2	syl 18	1 ⊢ (𝜑 → 𝐴 ∈ No)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2144  Nocsur 27998  ℝ_screno 28876

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-or 862  df-3an 1105  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-rex 3087  df-rab 3413  df-v 3452  df-ss 3896  df-dif 4047  df-un 4151  df-nul 4279  df-if 4482  df-sn 4584  df-pr 4586  df-op 4590  df-uni 4867  df-br 5103  df-iota 6494  df-fv 6546  df-ov 7423  df-reno 28877

This theorem is used by: (None)