Theorem modal-b 2142

Description: The analogue 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

Step	Hyp	Ref	Expression
1		axc7 2132	. 2 |- ( -. A. x -. A. x -. ph -> -. ph )
2	1	con4i 113	1 |- ( ph -> A. x -. A. x -. ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by:  bj-modalbe  32678