Theorem onnoi

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

	Ref	Expression
Hypothesis	onnoi.on	⊢ 𝐴 ∈ On
Assertion	onnoi	⊢ ( 𝐴 × { 2o } ) ∈ No

Proof

Step	Hyp	Ref	Expression
1		onnoi.on	⊢ 𝐴 ∈ On
2		onno	⊢ ( 𝐴 ∈ On → ( 𝐴 × { 2o } ) ∈ No )
3	1 2	ax-mp	⊢ ( 𝐴 × { 2o } ) ∈ No