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Theorem bj-19.3t 32814
Description: Closed form of 19.3 2107. (Contributed by BJ, 20-Oct-2019.)
Assertion
Ref Expression
bj-19.3t ((𝜑 → ∀𝑥𝜑) → (∀𝑥𝜑𝜑))

Proof of Theorem bj-19.3t
StepHypRef Expression
1 sp 2091 . 2 (∀𝑥𝜑𝜑)
2 id 22 . 2 ((𝜑 → ∀𝑥𝜑) → (𝜑 → ∀𝑥𝜑))
31, 2impbid2 216 1 ((𝜑 → ∀𝑥𝜑) → (∀𝑥𝜑𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wal 1521
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-12 2087
This theorem depends on definitions:  df-bi 197  df-ex 1745
This theorem is referenced by: (None)
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