Metamath Proof Explorer


Theorem 0sno

Description: Surreal zero is a surreal. (Contributed by Scott Fenton, 7-Aug-2024)

Ref Expression
Assertion 0sno Could not format assertion : No typesetting found for |- 0s e. No with typecode |-

Proof

Step Hyp Ref Expression
1 df-0s Could not format 0s = ( (/) |s (/) ) : No typesetting found for |- 0s = ( (/) |s (/) ) with typecode |-
2 0elpw 𝒫 No
3 nulssgt 𝒫 No s
4 2 3 ax-mp s
5 scutcl s | s No
6 4 5 ax-mp | s No
7 1 6 eqeltri Could not format 0s e. No : No typesetting found for |- 0s e. No with typecode |-