Metamath Proof Explorer


Theorem neutru

Description: There does not exist exactly one set such that T. is true. (Contributed by Anthony Hart, 13-Sep-2011)

Ref Expression
Assertion neutru ¬ ∃! x

Proof

Step Hyp Ref Expression
1 nexntru ¬ x ¬
2 eunex ∃! x x ¬
3 1 2 mto ¬ ∃! x