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Theorem impxt 24395
Description: If  ph  ->  ps holds unconditionally and if  ph holds in the next state then  ps holds in the next state. (Contributed by FL, 20-Mar-2011.)
Hypothesis
Ref Expression
impxt.1  |-  ( ph  ->  ps )
Assertion
Ref Expression
impxt  |-  ( ()
ph  ->  () ps )

Proof of Theorem impxt
StepHypRef Expression
1 impxt.1 . . 3  |-  ( ph  ->  ps )
21ax-nmp 24391 . 2  |-  () (
ph  ->  ps )
3 ax-ltl3 24388 . 2  |-  ( () ( ph  ->  ps )  ->  ( () ph  ->  () ps ) )
42, 3ax-mp 8 1  |-  ( ()
ph  ->  () ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   ()wcirc 24384
This theorem is referenced by:  binxt  24396  nxtor  24397  nxtand  24398  alne  24414
This theorem was proved from axioms:  ax-mp 8  ax-ltl3 24388  ax-nmp 24391
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