Metamath Proof Explorer


Theorem 1sno

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

Ref Expression
Assertion 1sno Could not format assertion : No typesetting found for |- 1s e. No with typecode |-

Proof

Step Hyp Ref Expression
1 df-1s Could not format 1s = ( { 0s } |s (/) ) : No typesetting found for |- 1s = ( { 0s } |s (/) ) with typecode |-
2 0sno Could not format 0s e. No : No typesetting found for |- 0s e. No with typecode |-
3 snelpwi Could not format ( 0s e. No -> { 0s } e. ~P No ) : No typesetting found for |- ( 0s e. No -> { 0s } e. ~P No ) with typecode |-
4 2 3 ax-mp Could not format { 0s } e. ~P No : No typesetting found for |- { 0s } e. ~P No with typecode |-
5 nulssgt Could not format ( { 0s } e. ~P No -> { 0s } < { 0s } <
6 4 5 ax-mp Could not format { 0s } <
7 scutcl Could not format ( { 0s } < ( { 0s } |s (/) ) e. No ) : No typesetting found for |- ( { 0s } < ( { 0s } |s (/) ) e. No ) with typecode |-
8 6 7 ax-mp Could not format ( { 0s } |s (/) ) e. No : No typesetting found for |- ( { 0s } |s (/) ) e. No with typecode |-
9 1 8 eqeltri Could not format 1s e. No : No typesetting found for |- 1s e. No with typecode |-