Theorem renod 28695

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 28694	. 2 ⊢ (𝐴 ∈ ℝs → 𝐴 ∈ No )
3	1, 2	syl 18	1 ⊢ (𝜑 → 𝐴 ∈ No )

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2143   No csur 27813  ℝ_screno 28691

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-rex 3090  df-rab 3417  df-v 3457  df-dif 3908  df-un 3910  df-ss 3922  df-nul 4287  df-if 4488  df-sn 4590  df-pr 4592  df-op 4596  df-uni 4873  df-br 5110  df-iota 6492  df-fv 6544  df-ov 7413  df-reno 28692

This theorem is used by: (None)