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Theorem bj-alrim 32910
Description: Closed form of alrimi 2193. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-alrim (Ⅎ𝑥𝜑 → (∀𝑥(𝜑𝜓) → (𝜑 → ∀𝑥𝜓)))

Proof of Theorem bj-alrim
StepHypRef Expression
1 nf5r 2175 . 2 (Ⅎ𝑥𝜑 → (𝜑 → ∀𝑥𝜑))
2 sylgt 1862 . 2 (∀𝑥(𝜑𝜓) → ((𝜑 → ∀𝑥𝜑) → (𝜑 → ∀𝑥𝜓)))
31, 2syl5com 31 1 (Ⅎ𝑥𝜑 → (∀𝑥(𝜑𝜓) → (𝜑 → ∀𝑥𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1594  wnf 1821
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-12 2160
This theorem depends on definitions:  df-bi 197  df-ex 1818  df-nf 1823
This theorem is referenced by:  bj-alrim2  32911
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