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Theorem phthps 24996
Description: If  ph doesn't hold in the current step and  ph holds until  ps then  ps holds in the current step. (Contributed by FL, 20-Mar-2011.)
Assertion
Ref Expression
phthps  |-  ( ( -.  ph  /\  ( ph  until  ps ) )  ->  ps )

Proof of Theorem phthps
StepHypRef Expression
1 nopsthph 24995 . . . 4  |-  ( ( -.  ps  /\  ( ph  until  ps ) )  ->  ph )
21expcom 424 . . 3  |-  ( (
ph  until  ps )  -> 
( -.  ps  ->  ph ) )
32con1d 116 . 2  |-  ( (
ph  until  ps )  -> 
( -.  ph  ->  ps ) )
43impcom 419 1  |-  ( ( -.  ph  /\  ( ph  until  ps ) )  ->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 358    until wunt 24973
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-ltl5 24993
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360
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