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 
|- ( ph -> A. x -. A. x -. ph )

Proof

Step Hyp Ref Expression
1 axc7 
 |-  ( -. A. x -. A. x -. ph -> -. ph )
2 1 con4i 
 |-  ( ph -> A. x -. A. x -. ph )