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Theorem imunt 24997
Description: If  ps is true, then  ph is true until  ps. (Contributed by Mario Carneiro, 30-Aug-2016.)
Assertion
Ref Expression
imunt  |-  ( ps 
->  ( ph  until  ps )
)

Proof of Theorem imunt
StepHypRef Expression
1 orc 374 . 2  |-  ( ps 
->  ( ps  \/  ( ph  /\  () ( ph  until  ps ) ) ) )
2 ax-ltl5 24993 . 2  |-  ( (
ph  until  ps )  <->  ( ps  \/  ( ph  /\  () ( ph  until  ps ) ) ) )
31, 2sylibr 203 1  |-  ( ps 
->  ( ph  until  ps )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 357    /\ wa 358   ()wcirc 24972    until wunt 24973
This theorem is referenced by:  unttr  25017
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
  Copyright terms: Public domain W3C validator