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