Theorem rightgt

Description: A member of a surreal's right set is greater than it. (Contributed by Scott Fenton, 7-Nov-2025)

	Ref	Expression
Assertion	rightgt	⊢ ( 𝐴 ∈ ( R ‘ 𝐵 ) → 𝐵 <s 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		elright	⊢ ( 𝐴 ∈ ( R ‘ 𝐵 ) ↔ ( 𝐴 ∈ ( O ‘ ( bday ‘ 𝐵 ) ) ∧ 𝐵 <s 𝐴 ) )
2	1	simprbi	⊢ ( 𝐴 ∈ ( R ‘ 𝐵 ) → 𝐵 <s 𝐴 )