Theorem rmo0

Description: Vacuous restricted at-most-one quantifier is always true. (Contributed by AV, 3-Apr-2023)

	Ref	Expression
Assertion	rmo0	⊢ ∃* 𝑥 ∈ ∅ 𝜑

Proof

Step	Hyp	Ref	Expression
1		rex0	⊢ ¬ ∃ 𝑥 ∈ ∅ 𝜑
2	1	pm2.21i	⊢ ( ∃ 𝑥 ∈ ∅ 𝜑 → ∃! 𝑥 ∈ ∅ 𝜑 )
3		rmo5	⊢ ( ∃* 𝑥 ∈ ∅ 𝜑 ↔ ( ∃ 𝑥 ∈ ∅ 𝜑 → ∃! 𝑥 ∈ ∅ 𝜑 ) )
4	2 3	mpbir	⊢ ∃* 𝑥 ∈ ∅ 𝜑