Metamath Proof Explorer


Definition df-1s

Description: Define surreal one. This is the simplest number greater than surreal zero. Definition from Conway p. 18. (Contributed by Scott Fenton, 7-Aug-2024)

Ref Expression
Assertion df-1s 1s = ( { 0s } |s ∅ )

Detailed syntax breakdown

Step Hyp Ref Expression
0 c1s 1s
1 c0s 0s
2 1 csn { 0s }
3 cscut |s
4 c0
5 2 4 3 co ( { 0s } |s ∅ )
6 0 5 wceq 1s = ( { 0s } |s ∅ )