Theorem nfdvOLD 1873

Description: Obsolete proof of nf5dv 2025 as of 6-Oct-2021. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
nfdvOLD.1	⊢ (𝜑 → (𝜓 → ∀𝑥𝜓))

Assertion

Ref	Expression
nfdvOLD	⊢ (𝜑 → Ⅎ𝑥𝜓)

Distinct variable group:   𝜑,𝑥

Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem nfdvOLD

Step	Hyp	Ref	Expression
1		nfdvOLD.1	. . 3 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜓))
2	1	alrimiv 1855	. 2 ⊢ (𝜑 → ∀𝑥(𝜓 → ∀𝑥𝜓))
3		df-nfOLD 1721	. 2 ⊢ (Ⅎ𝑥𝜓 ↔ ∀𝑥(𝜓 → ∀𝑥𝜓))
4	2, 3	sylibr 224	1 ⊢ (𝜑 → Ⅎ𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1481  ℲwnfOLD 1709

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839

This theorem depends on definitions:  df-bi 197  df-nfOLD 1721

This theorem is referenced by: (None)