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

Theorem modal-b 1768
Description: The analog in our predicate calculus of the Brouwer axiom (B) of modal logic S5. (Contributed by NM, 5-Oct-2005.)
Assertion
Ref Expression
modal-b  |-  ( ph  ->  A. x  -.  A. x  -.  ph )

Proof of Theorem modal-b
StepHypRef Expression
1 ax6o 1766 . 2  |-  ( -. 
A. x  -.  A. x  -.  ph  ->  -.  ph )
21con4i 124 1  |-  ( ph  ->  A. x  -.  A. x  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1549
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761
This theorem depends on definitions:  df-bi 178  df-ex 1551
  Copyright terms: Public domain W3C validator