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Theorem bj-modalb 32706
Description: A short form of the axiom B of modal logic. (Contributed by BJ, 4-Apr-2021.)
Assertion
Ref Expression
bj-modalb  |-  ( -. 
ph  ->  A. x  -.  A. x ph )

Proof of Theorem bj-modalb
StepHypRef Expression
1 axc7 2132 . 2  |-  ( -. 
A. x  -.  A. x ph  ->  ph )
21con1i 144 1  |-  ( -. 
ph  ->  A. x  -.  A. x ph )
Colors of variables: wff setvar class
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: (None)
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