Theorem 0no

Description: Ordinal zero maps to a surreal number. (Contributed by RP, 21-Sep-2023)

	Ref	Expression
Assertion	0no	⊢ ∅ ∈ No

Proof

Step	Hyp	Ref	Expression
1		0xp	⊢ ( ∅ × { 2o } ) = ∅
2		0elon	⊢ ∅ ∈ On
3	2	onnoi	⊢ ( ∅ × { 2o } ) ∈ No
4	1 3	eqeltrri	⊢ ∅ ∈ No