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Theorem bj-pm2.18st 12943
Description: Clavius law for stable formulas. See pm2.18dc 840. (Contributed by BJ, 4-Dec-2023.)
Assertion
Ref Expression
bj-pm2.18st  |-  (STAB  ph  ->  ( ( -.  ph  ->  ph )  ->  ph ) )

Proof of Theorem bj-pm2.18st
StepHypRef Expression
1 df-stab 816 . 2  |-  (STAB  ph  <->  ( -.  -.  ph  ->  ph ) )
2 bj-nnclavius 12935 . . 3  |-  ( ( -.  ph  ->  ph )  ->  -.  -.  ph )
32imim1i 60 . 2  |-  ( ( -.  -.  ph  ->  ph )  ->  ( ( -.  ph  ->  ph )  ->  ph ) )
41, 3sylbi 120 1  |-  (STAB  ph  ->  ( ( -.  ph  ->  ph )  ->  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4  STAB wstab 815
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-in1 603  ax-in2 604
This theorem depends on definitions:  df-bi 116  df-stab 816
This theorem is referenced by: (None)
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