ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  imp43 Unicode version

Theorem imp43 355
Description: An importation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
imp4.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
Assertion
Ref Expression
imp43  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  ->  ta )

Proof of Theorem imp43
StepHypRef Expression
1 imp4.1 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
21imp4b 350 . 2  |-  ( (
ph  /\  ps )  ->  ( ( ch  /\  th )  ->  ta )
)
32imp 124 1  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104
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
This theorem is referenced by:  fundmen  6862  fiintim  6987  divgt0  8893  divge0  8894  le2sq2  10689  islmodd  13792  islssmd  13858  basis2  14227  dvidlemap  14870  dvidrelem  14871  dvidsslem  14872
  Copyright terms: Public domain W3C validator