Theorem nfri

Description: Consequence of the definition of not-free. (Contributed by Wolf Lammen, 16-Sep-2021)

	Ref	Expression
Hypothesis	nfri.1	⊢ Ⅎ 𝑥 𝜑
Assertion	nfri	⊢ ( ∃ 𝑥 𝜑 → ∀ 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		nfri.1	⊢ Ⅎ 𝑥 𝜑
2		df-nf	⊢ ( Ⅎ 𝑥 𝜑 ↔ ( ∃ 𝑥 𝜑 → ∀ 𝑥 𝜑 ) )
3	1 2	mpbi	⊢ ( ∃ 𝑥 𝜑 → ∀ 𝑥 𝜑 )