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Theorem bj-bialal 32824
Description: A general FOL biconditional. (Contributed by BJ, 20-Oct-2019.)
Assertion
Ref Expression
bj-bialal (∀𝑥(∀𝑥𝜑𝜓) ↔ (∀𝑥𝜑 → ∀𝑥𝜓))

Proof of Theorem bj-bialal
StepHypRef Expression
1 nfa1 2068 . 2 𝑥𝑥𝜑
2119.21 2113 1 (∀𝑥(∀𝑥𝜑𝜓) ↔ (∀𝑥𝜑 → ∀𝑥𝜓))
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-10 2059  ax-12 2087
This theorem depends on definitions:  df-bi 197  df-or 384  df-ex 1745  df-nf 1750
This theorem is referenced by: (None)
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