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Theorem modal-5 2018
Description: The analogue in our predicate calculus of axiom (5) of modal logic S5. (Contributed by NM, 5-Oct-2005.)
Assertion
Ref Expression
modal-5 (¬ ∀𝑥 ¬ 𝜑 → ∀𝑥 ¬ ∀𝑥 ¬ 𝜑)

Proof of Theorem modal-5
StepHypRef Expression
1 hbn1 2006 1 (¬ ∀𝑥 ¬ 𝜑 → ∀𝑥 ¬ ∀𝑥 ¬ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1472
This theorem was proved from axioms:  ax-10 2005
This theorem is referenced by: (None)
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