Theorem reu0

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

	Ref	Expression
Assertion	reu0	⊢ ¬ ∃! 𝑥 ∈ ∅ 𝜑

Proof

Step	Hyp	Ref	Expression
1		rex0	⊢ ¬ ∃ 𝑥 ∈ ∅ 𝜑
2		reurex	⊢ ( ∃! 𝑥 ∈ ∅ 𝜑 → ∃ 𝑥 ∈ ∅ 𝜑 )
3	1 2	mto	⊢ ¬ ∃! 𝑥 ∈ ∅ 𝜑