Description: The undefined value generated from a set is not a member of the set. (Contributed by NM, 15-Sep-2011)
Ref | Expression | ||
---|---|---|---|
Assertion | undefnel2 | ⊢ ( 𝑆 ∈ 𝑉 → ¬ ( Undef ‘ 𝑆 ) ∈ 𝑆 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pwuninel | ⊢ ¬ 𝒫 ∪ 𝑆 ∈ 𝑆 | |
2 | undefval | ⊢ ( 𝑆 ∈ 𝑉 → ( Undef ‘ 𝑆 ) = 𝒫 ∪ 𝑆 ) | |
3 | 2 | eleq1d | ⊢ ( 𝑆 ∈ 𝑉 → ( ( Undef ‘ 𝑆 ) ∈ 𝑆 ↔ 𝒫 ∪ 𝑆 ∈ 𝑆 ) ) |
4 | 1 3 | mtbiri | ⊢ ( 𝑆 ∈ 𝑉 → ¬ ( Undef ‘ 𝑆 ) ∈ 𝑆 ) |