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Theorem modal5 2160
Description: The analogue in our predicate calculus of axiom (5) of modal logic S5. See also hbe1 2148. (Contributed by NM, 5-Oct-2005.)
Assertion
Ref Expression
modal5 (¬ ∀𝑥 ¬ 𝜑 → ∀𝑥 ¬ ∀𝑥 ¬ 𝜑)

Proof of Theorem modal5
StepHypRef Expression
1 hbn1 2147 1 (¬ ∀𝑥 ¬ 𝜑 → ∀𝑥 ¬ ∀𝑥 ¬ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1536
This theorem was proved from axioms:  ax-10 2146
This theorem is referenced by: (None)
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