Theorem modal-5 1590

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 1582	1 |- ( -. A. x -. ph -> A. x -. A. x -. ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1282

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577  ax-5 1376  ax-gen 1378  ax-ie2 1423  ax-ial 1467

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-fal 1290

This theorem is referenced by: (None)