MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  impac Structured version   Unicode version

Theorem impac 605
Description: Importation with conjunction in consequent. (Contributed by NM, 9-Aug-1994.)
Hypothesis
Ref Expression
impac.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
impac  |-  ( (
ph  /\  ps )  ->  ( ch  /\  ps ) )

Proof of Theorem impac
StepHypRef Expression
1 impac.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21ancrd 538 . 2  |-  ( ph  ->  ( ps  ->  ( ch  /\  ps ) ) )
32imp 419 1  |-  ( (
ph  /\  ps )  ->  ( ch  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359
This theorem is referenced by:  imdistanri  673  zfrep6  5968  f1elima  6009  tfrlem5  6641  sltval2  25611
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 178  df-an 361
  Copyright terms: Public domain W3C validator