Metamath Proof Explorer


Theorem undefnel

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 ( 𝑆𝑉 → ( Undef ‘ 𝑆 ) ∉ 𝑆 )

Proof

Step Hyp Ref Expression
1 undefnel2 ( 𝑆𝑉 → ¬ ( Undef ‘ 𝑆 ) ∈ 𝑆 )
2 df-nel ( ( Undef ‘ 𝑆 ) ∉ 𝑆 ↔ ¬ ( Undef ‘ 𝑆 ) ∈ 𝑆 )
3 1 2 sylibr ( 𝑆𝑉 → ( Undef ‘ 𝑆 ) ∉ 𝑆 )