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Theorem exp5j 26313
Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
exp5j.1  |-  ( ph  ->  ( ( ( ( ps  /\  ch )  /\  th )  /\  ta )  ->  et ) )
Assertion
Ref Expression
exp5j  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )

Proof of Theorem exp5j
StepHypRef Expression
1 exp5j.1 . . 3  |-  ( ph  ->  ( ( ( ( ps  /\  ch )  /\  th )  /\  ta )  ->  et ) )
21exp3a 425 . 2  |-  ( ph  ->  ( ( ( ps 
/\  ch )  /\  th )  ->  ( ta  ->  et ) ) )
32exp4c 591 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  exp510  26318
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