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Theorem binxt 24984
Description: If  ph  <->  ps holds unconditionally then  ph holds in the next state of the world iff  ps holds in the next state. (Contributed by FL, 20-Mar-2011.)
Hypothesis
Ref Expression
binxt.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
binxt  |-  ( ()
ph 
<->  () ps )

Proof of Theorem binxt
StepHypRef Expression
1 binxt.1 . . . 4  |-  ( ph  <->  ps )
21biimpi 186 . . 3  |-  ( ph  ->  ps )
32impxt 24983 . 2  |-  ( ()
ph  ->  () ps )
41biimpri 197 . . 3  |-  ( ps 
->  ph )
54impxt 24983 . 2  |-  ( () ps  ->  () ph )
63, 5impbii 180 1  |-  ( ()
ph 
<->  () ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 176   ()wcirc 24972
This theorem is referenced by:  nxtor  24985  albineal  24999
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-ltl3 24976  ax-nmp 24979
This theorem depends on definitions:  df-bi 177
  Copyright terms: Public domain W3C validator