Theorem nf5rOLD

Description: Obsolete version of nfrd as of 23-Nov-2023. (Contributed by Mario Carneiro, 26-Sep-2016) df-nf changed. (Revised by Wolf Lammen, 11-Sep-2021) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	nf5rOLD	⊢ ( Ⅎ 𝑥 𝜑 → ( 𝜑 → ∀ 𝑥 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		19.8a	⊢ ( 𝜑 → ∃ 𝑥 𝜑 )
2		df-nf	⊢ ( Ⅎ 𝑥 𝜑 ↔ ( ∃ 𝑥 𝜑 → ∀ 𝑥 𝜑 ) )
3	2	biimpi	⊢ ( Ⅎ 𝑥 𝜑 → ( ∃ 𝑥 𝜑 → ∀ 𝑥 𝜑 ) )
4	1 3	syl5	⊢ ( Ⅎ 𝑥 𝜑 → ( 𝜑 → ∀ 𝑥 𝜑 ) )