Theorem rightssold

Description: The right options are a subset of the old set. (Contributed by Scott Fenton, 9-Oct-2024)

	Ref	Expression
Assertion	rightssold	⊢ ( R ‘ 𝑋 ) ⊆ ( O ‘ ( bday ‘ 𝑋 ) )

Proof

Step	Hyp	Ref	Expression
1		rightval	⊢ ( R ‘ 𝑋 ) = { 𝑥 ∈ ( O ‘ ( bday ‘ 𝑋 ) ) ∣ 𝑋 <s 𝑥 }
2		ssrab2	⊢ { 𝑥 ∈ ( O ‘ ( bday ‘ 𝑋 ) ) ∣ 𝑋 <s 𝑥 } ⊆ ( O ‘ ( bday ‘ 𝑋 ) )
3	1 2	eqsstri	⊢ ( R ‘ 𝑋 ) ⊆ ( O ‘ ( bday ‘ 𝑋 ) )