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Theorem alne 25002
Description: If  ph always holds, it holds in the next step. (Contributed by FL, 20-Mar-2011.)
Assertion
Ref Expression
alne  |-  ( [.] ph  ->  () ph )

Proof of Theorem alne
StepHypRef Expression
1 alneal2 25001 . 2  |-  ( [.] ph  ->  () [.] ph )
2 alneal1 25000 . . 3  |-  ( [.] ph  ->  ph )
32impxt 24983 . 2  |-  ( ()
[.] ph  ->  () ph )
41, 3syl 15 1  |-  ( [.] ph  ->  () ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   [.]wbox 24970   ()wcirc 24972
This theorem is referenced by:  nxtimd  25009  althalne  25015
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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