Description: Surreal one is a surreal. (Contributed by Scott Fenton, 7-Aug-2024)
Ref | Expression | ||
---|---|---|---|
Assertion | 1sno | ⊢ 1s ∈ No |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-1s | ⊢ 1s = ( { 0s } |s ∅ ) | |
2 | 0sno | ⊢ 0s ∈ No | |
3 | snelpwi | ⊢ ( 0s ∈ No → { 0s } ∈ 𝒫 No ) | |
4 | 2 3 | ax-mp | ⊢ { 0s } ∈ 𝒫 No |
5 | nulssgt | ⊢ ( { 0s } ∈ 𝒫 No → { 0s } <<s ∅ ) | |
6 | 4 5 | ax-mp | ⊢ { 0s } <<s ∅ |
7 | scutcl | ⊢ ( { 0s } <<s ∅ → ( { 0s } |s ∅ ) ∈ No ) | |
8 | 6 7 | ax-mp | ⊢ ( { 0s } |s ∅ ) ∈ No |
9 | 1 8 | eqeltri | ⊢ 1s ∈ No |