Theorem reu0

Description: Vacuous restricted uniqueness is always false. (Contributed by AV, 3-Apr-2023)

	Ref	Expression
Assertion	reu0	$$⊢\neg \exists !x\in \varnothing \phi$$

Proof

Step	Hyp	Ref	Expression
1		rex0	$$⊢\neg \exists x\in \varnothing \phi$$
2		reurex	$$⊢\exists !x\in \varnothing \phi \to \exists x\in \varnothing \phi$$
3	1 2	mto	$$⊢\neg \exists !x\in \varnothing \phi$$