MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  modal-5 Unicode version

Theorem modal-5 1707
Description: The analog in our "pure" predicate calculus of axiom 5 of modal logic S5. (Contributed by NM, 5-Oct-2005.)
Assertion
Ref Expression
modal-5  |-  ( -. 
A. x  -.  ph  ->  A. x  -.  A. x  -.  ph )

Proof of Theorem modal-5
StepHypRef Expression
1 hbn1 1704 1  |-  ( -. 
A. x  -.  ph  ->  A. x  -.  A. x  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1527
This theorem was proved from axioms:  ax-6 1703
  Copyright terms: Public domain W3C validator