Theorem modal-5 1550

Description: The analog in our 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

Step	Hyp	Ref	Expression
1		hbn1 1542	1 |- ( -. A. x -. ph -> A. x -. A. x -. ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1241

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-ie2 1383  ax-ial 1427

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249

This theorem is referenced by: (None)