Theorem nfrOLD 2186

Description: Obsolete proof of nf5r 2062 as of 6-Oct-2021. (Contributed by Mario Carneiro, 26-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
nfrOLD	⊢ (Ⅎ𝑥𝜑 → (𝜑 → ∀𝑥𝜑))

Proof of Theorem nfrOLD

Step	Hyp	Ref	Expression
1		df-nfOLD 1719	. 2 ⊢ (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑))
2		sp 2051	. 2 ⊢ (∀𝑥(𝜑 → ∀𝑥𝜑) → (𝜑 → ∀𝑥𝜑))
3	1, 2	sylbi 207	1 ⊢ (Ⅎ𝑥𝜑 → (𝜑 → ∀𝑥𝜑))

Syntax hints:   → wi 4  ∀wal 1479  ℲwnfOLD 1707

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-12 2045

This theorem depends on definitions:  df-bi 197  df-ex 1703  df-nfOLD 1719

This theorem is referenced by:  nfriOLD  2187  nfrdOLD  2188  19.21t-1OLD  2210  nfimdOLD  2224