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 
|- ( S e. V -> ( Undef ` S ) e/ S )

Proof

Step Hyp Ref Expression
1 undefnel2 
 |-  ( S e. V -> -. ( Undef ` S ) e. S )
2 df-nel 
 |-  ( ( Undef ` S ) e/ S <-> -. ( Undef ` S ) e. S )
3 1 2 sylibr 
 |-  ( S e. V -> ( Undef ` S ) e/ S )