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Theorem nf5rOLD 2195
Description: Obsolete version of nfrd 1793 as of 23-Nov-2023. (Contributed by Mario Carneiro, 26-Sep-2016.) df-nf 1786 changed. (Revised by Wolf Lammen, 11-Sep-2021.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
nf5rOLD (Ⅎ𝑥𝜑 → (𝜑 → ∀𝑥𝜑))

Proof of Theorem nf5rOLD
StepHypRef Expression
1 19.8a 2181 . 2 (𝜑 → ∃𝑥𝜑)
2 df-nf 1786 . . 3 (Ⅎ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
32biimpi 219 . 2 (Ⅎ𝑥𝜑 → (∃𝑥𝜑 → ∀𝑥𝜑))
41, 3syl5 34 1 (Ⅎ𝑥𝜑 → (𝜑 → ∀𝑥𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1536  wex 1781  wnf 1785
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-12 2178
This theorem depends on definitions:  df-bi 210  df-ex 1782  df-nf 1786
This theorem is referenced by: (None)
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