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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
StepHypRef Expression
1 df-nfOLD 1719 . 2 (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑))
2 sp 2051 . 2 (∀𝑥(𝜑 → ∀𝑥𝜑) → (𝜑 → ∀𝑥𝜑))
31, 2sylbi 207 1 (Ⅎ𝑥𝜑 → (𝜑 → ∀𝑥𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1479  wnfOLD 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
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