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Theorem bj-2albi 34532
Description: Closed form of 2albii 1828. (Contributed by BJ, 6-May-2019.)
Assertion
Ref Expression
bj-2albi (∀𝑥𝑦(𝜑𝜓) → (∀𝑥𝑦𝜑 ↔ ∀𝑥𝑦𝜓))

Proof of Theorem bj-2albi
StepHypRef Expression
1 albi 1826 . . 3 (∀𝑦(𝜑𝜓) → (∀𝑦𝜑 ↔ ∀𝑦𝜓))
21alimi 1819 . 2 (∀𝑥𝑦(𝜑𝜓) → ∀𝑥(∀𝑦𝜑 ↔ ∀𝑦𝜓))
3 albi 1826 . 2 (∀𝑥(∀𝑦𝜑 ↔ ∀𝑦𝜓) → (∀𝑥𝑦𝜑 ↔ ∀𝑥𝑦𝜓))
42, 3syl 17 1 (∀𝑥𝑦(𝜑𝜓) → (∀𝑥𝑦𝜑 ↔ ∀𝑥𝑦𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209  wal 1541
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817
This theorem depends on definitions:  df-bi 210
This theorem is referenced by: (None)
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