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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 ⊥