Theorem modal-b 1752

Description: The analog in our "pure" predicate calculus of the Brouwer axiom (B) of modal logic S5. (Contributed by NM, 5-Oct-2005.)

Assertion

Ref	Expression
modal-b	⊢ (φ → ∀x ¬ ∀x ¬ φ)

Proof of Theorem modal-b

Step	Hyp	Ref	Expression
1		ax6o 1750	. 2 ⊢ (¬ ∀x ¬ ∀x ¬ φ → ¬ φ)
2	1	con4i 122	1 ⊢ (φ → ∀x ¬ ∀x ¬ φ)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by: (None)