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Theorem exp511 30523
Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
exp511.1  |-  ( (
ph  /\  ( ( ps  /\  ( ch  /\  th ) )  /\  ta ) )  ->  et )
Assertion
Ref Expression
exp511  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )

Proof of Theorem exp511
StepHypRef Expression
1 exp511.1 . . 3  |-  ( (
ph  /\  ( ( ps  /\  ( ch  /\  th ) )  /\  ta ) )  ->  et )
21ex 432 . 2  |-  ( ph  ->  ( ( ( ps 
/\  ( ch  /\  th ) )  /\  ta )  ->  et ) )
32exp5k 30518 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 369
This theorem is referenced by: (None)
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