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Theorem exp5o 1214
Description: A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)
Hypothesis
Ref Expression
exp5o.1  |-  ( (
ph  /\  ps  /\  ch )  ->  ( ( th 
/\  ta )  ->  et ) )
Assertion
Ref Expression
exp5o  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )

Proof of Theorem exp5o
StepHypRef Expression
1 exp5o.1 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  ( ( th 
/\  ta )  ->  et ) )
21expd 434 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  ( th  ->  ( ta  ->  et )
) )
323exp 1194 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367    /\ w3a 972
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  df-3an 974
This theorem is referenced by:  exp520  1216  bndndx  10753  elicc3  30528
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