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Theorem althalne 24427
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 24414 . 2  |-  ( [.] ph  ->  () ph )
21boxrim 24419 1  |-  ( [.] ph  ->  [.] () ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   [.]wbox 24382   ()wcirc 24384
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-ltl1 24386  ax-ltl2 24387  ax-ltl3 24388  ax-ltl4 24389  ax-lmp 24390  ax-nmp 24391  ax-ltl5 24405  ax-ltl6 24406
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-dia 24392
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