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Theorem 3impexp 1227
Description: Version of impexp 447 for a triple conjunction. (Contributed by Alan Sare, 31-Dec-2011.)
Assertion
Ref Expression
3impexp  |-  ( ( ( ph  /\  ps  /\ 
ch )  ->  th )  <->  (
ph  ->  ( ps  ->  ( ch  ->  th )
) ) )

Proof of Theorem 3impexp
StepHypRef Expression
1 id 23 . . 3  |-  ( ( ( ph  /\  ps  /\ 
ch )  ->  th )  ->  ( ( ph  /\  ps  /\  ch )  ->  th ) )
213expd 1222 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  ->  th )  ->  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) ) )
3 id 23 . . 3  |-  ( (
ph  ->  ( ps  ->  ( ch  ->  th )
) )  ->  ( ph  ->  ( ps  ->  ( ch  ->  th )
) ) )
433impd 1219 . 2  |-  ( (
ph  ->  ( ps  ->  ( ch  ->  th )
) )  ->  (
( ph  /\  ps  /\  ch )  ->  th )
)
52, 4impbii 190 1  |-  ( ( ( ph  /\  ps  /\ 
ch )  ->  th )  <->  (
ph  ->  ( ps  ->  ( ch  ->  th )
) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187    /\ w3a 982
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 188  df-an 372  df-3an 984
This theorem is referenced by:  cotr2g  13019  bnj978  29548  3impexpbicom  36471  3impexpbicomVD  36893
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