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Theorem bj-alrim2 34613
Description: Uncurried (imported) form of bj-alrim 34612. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-alrim2 ((Ⅎ𝑥𝜑 ∧ ∀𝑥(𝜑𝜓)) → (𝜑 → ∀𝑥𝜓))

Proof of Theorem bj-alrim2
StepHypRef Expression
1 bj-alrim 34612 . 2 (Ⅎ𝑥𝜑 → (∀𝑥(𝜑𝜓) → (𝜑 → ∀𝑥𝜓)))
21imp 410 1 ((Ⅎ𝑥𝜑 ∧ ∀𝑥(𝜑𝜓)) → (𝜑 → ∀𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  wal 1541  wnf 1791
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-12 2175
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1788  df-nf 1792
This theorem is referenced by: (None)
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