Theorem addsid1d

Description: Surreal addition to zero is identity. Part of Theorem 3 of Conway p. 17. (Contributed by Scott Fenton, 20-Aug-2024)

	Ref	Expression
Hypothesis	addsid1d.1	⊢ ( 𝜑 → 𝐴 ∈ No )
Assertion	addsid1d	⊢ ( 𝜑 → ( 𝐴 +s 0s ) = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		addsid1d.1	⊢ ( 𝜑 → 𝐴 ∈ No )
2		addsid1	⊢ ( 𝐴 ∈ No → ( 𝐴 +s 0s ) = 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 +s 0s ) = 𝐴 )