Theorem r19.3rzv

Description: Restricted quantification of wff not containing quantified variable. (Contributed by NM, 10-Mar-1997)

	Ref	Expression
Assertion	r19.3rzv	⊢ ( 𝐴 ≠ ∅ → ( 𝜑 ↔ ∀ 𝑥 ∈ 𝐴 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		nfv	⊢ Ⅎ 𝑥 𝜑
2	1	r19.3rz	⊢ ( 𝐴 ≠ ∅ → ( 𝜑 ↔ ∀ 𝑥 ∈ 𝐴 𝜑 ) )