Metamath Proof Explorer


Theorem undefnel2

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

Proof

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