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Theorem alneal2 25001
Description: If  ph always holds, it always holds in the next step. (Contributed by FL, 20-Mar-2011.)
Assertion
Ref Expression
alneal2  |-  ( [.] ph  ->  () [.] ph )

Proof of Theorem alneal2
StepHypRef Expression
1 albineal 24999 . 2  |-  ( [.] ph 
<->  ( ph  /\  () [.] ph ) )
21simprbi 450 1  |-  ( [.] ph  ->  () [.] ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   [.]wbox 24970   ()wcirc 24972
This theorem is referenced by:  alne  25002  alalifal  25003
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-ltl1 24974  ax-ltl2 24975  ax-ltl3 24976  ax-ltl4 24977  ax-lmp 24978  ax-nmp 24979  ax-ltl5 24993  ax-ltl6 24994
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-dia 24980
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