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Theorem modal-b 1760
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 ax6o 1758 . 2  |-  ( -. 
A. x  -.  A. x  -.  ph  ->  -.  ph )
21con4i 124 1  |-  ( ph  ->  A. x  -.  A. x  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1546
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-11 1753
This theorem depends on definitions:  df-bi 178  df-ex 1548
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