Description: No surreal is a member of its right set. (Contributed by Scott Fenton, 20-Aug-2024)
Ref | Expression | ||
---|---|---|---|
Assertion | rightirr | ⊢ ( 𝑋 ∈ No → ¬ 𝑋 ∈ ( R ‘ 𝑋 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oldirr | ⊢ ¬ 𝑋 ∈ ( O ‘ ( bday ‘ 𝑋 ) ) | |
2 | rightssold | ⊢ ( 𝑋 ∈ No → ( R ‘ 𝑋 ) ⊆ ( O ‘ ( bday ‘ 𝑋 ) ) ) | |
3 | 2 | sseld | ⊢ ( 𝑋 ∈ No → ( 𝑋 ∈ ( R ‘ 𝑋 ) → 𝑋 ∈ ( O ‘ ( bday ‘ 𝑋 ) ) ) ) |
4 | 1 3 | mtoi | ⊢ ( 𝑋 ∈ No → ¬ 𝑋 ∈ ( R ‘ 𝑋 ) ) |