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Theorem modal-b 1915
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 axc7 1913 . 2  |-  ( -. 
A. x  -.  A. x  -.  ph  ->  -.  ph )
21con4i 134 1  |-  ( ph  ->  A. x  -.  A. x  -.  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1436
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-12 1906
This theorem depends on definitions:  df-bi 189  df-ex 1661
This theorem is referenced by:  bj-modalbe  31235
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