Theorem rex0

Description: Vacuous restricted existential quantification is false. (Contributed by NM, 15-Oct-2003)

	Ref	Expression
Assertion	rex0	⊢ ¬ ∃ 𝑥 ∈ ∅ 𝜑

Proof

Step	Hyp	Ref	Expression
1		noel	⊢ ¬ 𝑥 ∈ ∅
2	1	pm2.21i	⊢ ( 𝑥 ∈ ∅ → ¬ 𝜑 )
3	2	nrex	⊢ ¬ ∃ 𝑥 ∈ ∅ 𝜑