Description: The undefined value generated from a set is not a member of the set. (Contributed by NM, 15-Sep-2011)
Ref | Expression | ||
---|---|---|---|
Assertion | undefnel | ⊢ ( 𝑆 ∈ 𝑉 → ( Undef ‘ 𝑆 ) ∉ 𝑆 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | undefnel2 | ⊢ ( 𝑆 ∈ 𝑉 → ¬ ( Undef ‘ 𝑆 ) ∈ 𝑆 ) | |
2 | df-nel | ⊢ ( ( Undef ‘ 𝑆 ) ∉ 𝑆 ↔ ¬ ( Undef ‘ 𝑆 ) ∈ 𝑆 ) | |
3 | 1 2 | sylibr | ⊢ ( 𝑆 ∈ 𝑉 → ( Undef ‘ 𝑆 ) ∉ 𝑆 ) |