Theorem modal-5 1648

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 1640	1 |- ( -. A. x -. ph -> A. x -. A. x -. ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1341

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-5 1435  ax-gen 1437  ax-ie2 1482  ax-ial 1522

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-fal 1349

This theorem is referenced by: (None)