Description: The right options are a subset of the old set. (Contributed by Scott Fenton, 7-Aug-2024)
Ref | Expression | ||
---|---|---|---|
Assertion | rightssold | ⊢ ( 𝑋 ∈ No → ( R ‘ 𝑋 ) ⊆ ( O ‘ ( bday ‘ 𝑋 ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rightval | ⊢ ( 𝑋 ∈ No → ( R ‘ 𝑋 ) = { 𝑥 ∈ ( O ‘ ( bday ‘ 𝑋 ) ) ∣ 𝑋 <s 𝑥 } ) | |
2 | ssrab2 | ⊢ { 𝑥 ∈ ( O ‘ ( bday ‘ 𝑋 ) ) ∣ 𝑋 <s 𝑥 } ⊆ ( O ‘ ( bday ‘ 𝑋 ) ) | |
3 | 1 2 | eqsstrdi | ⊢ ( 𝑋 ∈ No → ( R ‘ 𝑋 ) ⊆ ( O ‘ ( bday ‘ 𝑋 ) ) ) |