Metamath Proof Explorer


Theorem modal-b

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

Ref Expression
Assertion modal-b φx¬x¬φ

Proof

Step Hyp Ref Expression
1 axc7 ¬x¬x¬φ¬φ
2 1 con4i φx¬x¬φ