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Theorem 19.3t 2202
Description: Closed form of 19.3 2203 and version of 19.9t 2205 with a universal quantifier. (Contributed by NM, 9-Nov-2020.) (Proof shortened by BJ, 9-Oct-2022.)
Assertion
Ref Expression
19.3t (Ⅎ𝑥𝜑 → (∀𝑥𝜑𝜑))

Proof of Theorem 19.3t
StepHypRef Expression
1 sp 2183 . 2 (∀𝑥𝜑𝜑)
2 nf5r 2194 . 2 (Ⅎ𝑥𝜑 → (𝜑 → ∀𝑥𝜑))
31, 2impbid2 229 1 (Ⅎ𝑥𝜑 → (∀𝑥𝜑𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209  wal 1536  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 1911  ax-6 1970  ax-7 2015  ax-12 2178
This theorem depends on definitions:  df-bi 210  df-ex 1782  df-nf 1786
This theorem is referenced by:  19.23t  2211
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