Theorem renod 28504

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 28503	. 2 ⊢ (𝐴 ∈ ℝs → 𝐴 ∈ No )
3	1, 2	syl 17	1 ⊢ (𝜑 → 𝐴 ∈ No )

Syntax hints:   → wi 4   ∈ wcel 2119   No csur 27622  ℝ_screno 28500

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-3an 1094  df-tru 1550  df-fal 1560  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-rex 3064  df-rab 3392  df-v 3433  df-dif 3886  df-un 3888  df-ss 3900  df-nul 4263  df-if 4456  df-sn 4557  df-pr 4559  df-op 4563  df-uni 4840  df-br 5074  df-iota 6442  df-fv 6494  df-ov 7360  df-reno 28501

This theorem is referenced by: (None)