ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3exp2 Unicode version

Theorem 3exp2 1225
Description: Exportation from right triple conjunction. (Contributed by NM, 26-Oct-2006.)
Hypothesis
Ref Expression
3exp2.1  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  ta )
Assertion
Ref Expression
3exp2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )

Proof of Theorem 3exp2
StepHypRef Expression
1 3exp2.1 . . 3  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  ta )
21ex 115 . 2  |-  ( ph  ->  ( ( ps  /\  ch  /\  th )  ->  ta ) )
323expd 1224 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    /\ w3a 978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 980
This theorem is referenced by:  3anassrs  1229  po2nr  4305  fliftfund  5791  tfrlemibxssdm  6321  tfr1onlembxssdm  6337  tfrcllembxssdm  6350  grpinveu  12788  grpid  12789  grpasscan1  12809  isxmetd  13480  dvidlemap  13793
  Copyright terms: Public domain W3C validator