Metamath Proof Explorer


Theorem newnod

Description: An element of a new set is a surreal. (Contributed by Scott Fenton, 27-Feb-2026)

Ref Expression
Hypothesis newnod.1 ⊢ ( 𝜑 → 𝐴 ∈ ( N ‘ 𝐵 ) )
Assertion newnod ( 𝜑 → 𝐴 ∈ No )

Proof

Step Hyp Ref Expression
1 newnod.1 ⊢ ( 𝜑 → 𝐴 ∈ ( N ‘ 𝐵 ) )
2 newssno ⊢ ( N ‘ 𝐵 ) ⊆ No
3 2 1 sselid ⊢ ( 𝜑 → 𝐴 ∈ No )