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Theorem exp5k 26314
Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
exp5k.1  |-  ( ph  ->  ( ( ( ps 
/\  ( ch  /\  th ) )  /\  ta )  ->  et ) )
Assertion
Ref Expression
exp5k  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )

Proof of Theorem exp5k
StepHypRef Expression
1 exp5k.1 . . 3  |-  ( ph  ->  ( ( ( ps 
/\  ( ch  /\  th ) )  /\  ta )  ->  et ) )
21exp3a 425 . 2  |-  ( ph  ->  ( ( ps  /\  ( ch  /\  th )
)  ->  ( ta  ->  et ) ) )
32exp4d 592 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  exp511  26319
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