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Theorem boximd 25111
Description: Distribute 'always' over implication when the context is always true. (Contributed by Mario Carneiro, 30-Aug-2016.)
Hypothesis
Ref Expression
boximd.1  |-  ( [.] ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
boximd  |-  ( [.] ph  ->  ( [.] ps  ->  [.] ch ) )

Proof of Theorem boximd
StepHypRef Expression
1 boximd.1 . . 3  |-  ( [.] ph  ->  ( ps  ->  ch ) )
21boxrim 25110 . 2  |-  ( [.] ph  ->  [.] ( ps  ->  ch ) )
3 ax-ltl1 25077 . 2  |-  ( [.] ( ps  ->  ch )  ->  ( [.] ps  ->  [.] ch ) )
42, 3syl 15 1  |-  ( [.] ph  ->  ( [.] ps  ->  [.] ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   [.]wbox 25073
This theorem is referenced by:  diaimd  25113  boxbid  25114
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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