Theorem old0

Description: No surreal is older than (/) . (Contributed by Scott Fenton, 7-Aug-2024)

	Ref	Expression
Assertion	old0	$$⊢\mathrm{Old}\left(\varnothing \right)=\varnothing$$

Proof

Step	Hyp	Ref	Expression
1		0elon	$$⊢\varnothing \in \mathrm{On}$$
2		oldval	Could not format ( (/) e. On -> ( _Old ` (/) ) = U. ( _Made " (/) ) ) : No typesetting found for |- ( (/) e. On -> ( _Old ` (/) ) = U. ( _Made " (/) ) ) with typecode |-
3	1 2	ax-mp	Could not format ( _Old ` (/) ) = U. ( _Made " (/) ) : No typesetting found for |- ( _Old ` (/) ) = U. ( _Made " (/) ) with typecode |-
4		ima0	Could not format ( _Made " (/) ) = (/) : No typesetting found for |- ( _Made " (/) ) = (/) with typecode |-
5	4	unieqi	Could not format U. ( _Made " (/) ) = U. (/) : No typesetting found for |- U. ( _Made " (/) ) = U. (/) with typecode |-
6		uni0	$$⊢\bigcup \varnothing =\varnothing$$
7	3 5 6	3eqtri	$$⊢\mathrm{Old}\left(\varnothing \right)=\varnothing$$