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Theorem bj-modalb 34158
Description: A short form of the axiom B of modal logic using only primitive symbols (→ , ¬ , ∀). (Contributed by BJ, 4-Apr-2021.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-modalb 𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)

Proof of Theorem bj-modalb
StepHypRef Expression
1 axc7 2328 . 2 (¬ ∀𝑥 ¬ ∀𝑥𝜑𝜑)
21con1i 149 1 𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1536
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2143  ax-12 2176
This theorem depends on definitions:  df-bi 210  df-ex 1782
This theorem is referenced by: (None)
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