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Metamath Proof Explorer

Theorem r19.3rzvOLD

Description: Obsolete version of r19.3rzv as of 16-Feb-2026. (Contributed by NM, 10-Mar-1997) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

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