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Theorem imp5d 582
Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
imp5.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
Assertion
Ref Expression
imp5d  |-  ( ( ( ph  /\  ps )  /\  ch )  -> 
( ( th  /\  ta )  ->  et ) )

Proof of Theorem imp5d
StepHypRef Expression
1 imp5.1 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
21imp31 421 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  -> 
( th  ->  ( ta  ->  et ) ) )
32imp3a 420 1  |-  ( ( ( ph  /\  ps )  /\  ch )  -> 
( ( th  /\  ta )  ->  et ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  bcthlem5  18766
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
  Copyright terms: Public domain W3C validator