Theorem ral0

Description: Vacuous universal quantification is always true. (Contributed by NM, 20-Oct-2005)

	Ref	Expression
Assertion	ral0	⊢ ∀ 𝑥 ∈ ∅ 𝜑

Proof

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