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Theorem boximd 24420
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 24419 . 2  |-  ( [.] ph  ->  [.] ( ps  ->  ch ) )
3 ax-ltl1 24386 . 2  |-  ( [.] ( ps  ->  ch )  ->  ( [.] ps  ->  [.] ch ) )
42, 3syl 15 1  |-  ( [.] ph  ->  ( [.] ps  ->  [.] ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   [.]wbox 24382
This theorem is referenced by:  diaimd  24422  boxbid  24423
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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