Metamath Proof Explorer


Theorem neufal

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

Ref Expression
Assertion neufal ¬ ∃! 𝑥

Proof

Step Hyp Ref Expression
1 nexfal ¬ ∃ 𝑥
2 euex ( ∃! 𝑥 ⊥ → ∃ 𝑥 ⊥ )
3 1 2 mto ¬ ∃! 𝑥