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Theorem althalne 25118
Description: If  ph is always true, then it is always true that  ph holds in the next step. (Contributed by FL, 20-Mar-2011.) (Proof shortened by Mario Carneiro, 30-Aug-2016.)
Assertion
Ref Expression
althalne  |-  ( [.] ph  ->  [.] () ph )

Proof of Theorem althalne
StepHypRef Expression
1 alne 25105 . 2  |-  ( [.] ph  ->  () ph )
21boxrim 25110 1  |-  ( [.] ph  ->  [.] () ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   [.]wbox 25073   ()wcirc 25075
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-ltl1 25077  ax-ltl2 25078  ax-ltl3 25079  ax-ltl4 25080  ax-lmp 25081  ax-nmp 25082  ax-ltl5 25096  ax-ltl6 25097
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-dia 25083
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