ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  imp4a Unicode version

Theorem imp4a 347
Description: An importation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
imp4.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
Assertion
Ref Expression
imp4a  |-  ( ph  ->  ( ps  ->  (
( ch  /\  th )  ->  ta ) ) )

Proof of Theorem imp4a
StepHypRef Expression
1 imp4.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
2 impexp 261 . 2  |-  ( ( ( ch  /\  th )  ->  ta )  <->  ( ch  ->  ( th  ->  ta ) ) )
31, 2syl6ibr 161 1  |-  ( ph  ->  ( ps  ->  (
( ch  /\  th )  ->  ta ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  imp4b  348  imp4d  350  imp55  359  imp511  360  equs5or  1810  reuss2  3387  tfrlem9  6266  facwordi  10614  ndvdssub  11821  neibl  12902
  Copyright terms: Public domain W3C validator