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 ⊥