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Theorem stdpc5t 33149
Description: Closed form of stdpc5 2232. (Possible to place it before 19.21t 2229 and use it to prove 19.21t 2229). (Contributed by BJ, 15-Sep-2018.) (Proof modification is discouraged.)
Assertion
Ref Expression
stdpc5t (Ⅎ𝑥𝜑 → (∀𝑥(𝜑𝜓) → (𝜑 → ∀𝑥𝜓)))

Proof of Theorem stdpc5t
StepHypRef Expression
1 nf5r 2218 . 2 (Ⅎ𝑥𝜑 → (𝜑 → ∀𝑥𝜑))
2 alim 1886 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓))
31, 2syl9 77 1 (Ⅎ𝑥𝜑 → (∀𝑥(𝜑𝜓) → (𝜑 → ∀𝑥𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1629  wnf 1856
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-12 2203
This theorem depends on definitions:  df-bi 197  df-ex 1853  df-nf 1858
This theorem is referenced by:  bj-stdpc5  33150  bj-19.21t  33152
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