Theorem renod 28506

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 28505	. 2 ⊢ (𝐴 ∈ ℝs → 𝐴 ∈ No )
3	1, 2	syl 17	1 ⊢ (𝜑 → 𝐴 ∈ No )

Syntax hints:   → wi 4   ∈ wcel 2114   No csur 27624  ℝ_screno 28502

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rex 3063  df-rab 3402  df-v 3444  df-dif 3906  df-un 3908  df-ss 3920  df-nul 4288  df-if 4482  df-sn 4583  df-pr 4585  df-op 4589  df-uni 4866  df-br 5101  df-iota 6458  df-fv 6510  df-ov 7373  df-reno 28503

This theorem is referenced by: (None)