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Theorem exp516 1171
Description: A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)
Hypothesis
Ref Expression
exp516.1  |-  ( ( ( ph  /\  ( ps  /\  ch  /\  th ) )  /\  ta )  ->  et )
Assertion
Ref Expression
exp516  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )

Proof of Theorem exp516
StepHypRef Expression
1 exp516.1 . . 3  |-  ( ( ( ph  /\  ( ps  /\  ch  /\  th ) )  /\  ta )  ->  et )
21exp31 587 . 2  |-  ( ph  ->  ( ( ps  /\  ch  /\  th )  -> 
( ta  ->  et ) ) )
323expd 1168 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
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  df-3an 936
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