Metamath Proof Explorer

Theorem modal5

Description: The analogue in our predicate calculus of axiom (5) of modal logic S5. See also hbe1 . (Contributed by NM, 5-Oct-2005)

Ref Expression
Assertion modal5 
|- ( -. A. x -. ph -> A. x -. A. x -. ph )

Proof

Step Hyp Ref Expression
1 hbn1 
 |-  ( -. A. x -. ph -> A. x -. A. x -. ph )