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Mirrors > Home > MPE Home > Th. List > modal-b | Structured version Visualization version GIF version |
Description: The analogue in our predicate calculus of the Brouwer axiom (B) of modal logic S5. (Contributed by NM, 5-Oct-2005.) |
Ref | Expression |
---|---|
modal-b | ⊢ (𝜑 → ∀𝑥 ¬ ∀𝑥 ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axc7 2117 | . 2 ⊢ (¬ ∀𝑥 ¬ ∀𝑥 ¬ 𝜑 → ¬ 𝜑) | |
2 | 1 | con4i 112 | 1 ⊢ (𝜑 → ∀𝑥 ¬ ∀𝑥 ¬ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1473 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-12 2034 |
This theorem depends on definitions: df-bi 196 df-ex 1696 |
This theorem is referenced by: bj-modalbe 31865 |
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