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Theorem exp520 1172
Description: A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)
Hypothesis
Ref Expression
exp520.1  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  ( th  /\  ta ) )  ->  et )
Assertion
Ref Expression
exp520  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )

Proof of Theorem exp520
StepHypRef Expression
1 exp520.1 . . 3  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  ( th  /\  ta ) )  ->  et )
21ex 423 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  ( ( th 
/\  ta )  ->  et ) )
32exp5o 1170 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
This theorem is referenced by:  omwordri  6586  oewordri  6606  pclfinclN  30761
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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