ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  mpbi2and Unicode version

Theorem mpbi2and 938
Description: Detach a conjunction of truths in a biconditional. (Contributed by NM, 6-Nov-2011.) (Proof shortened by Wolf Lammen, 24-Nov-2012.)
Hypotheses
Ref Expression
mpbi2and.1  |-  ( ph  ->  ps )
mpbi2and.2  |-  ( ph  ->  ch )
mpbi2and.3  |-  ( ph  ->  ( ( ps  /\  ch )  <->  th ) )
Assertion
Ref Expression
mpbi2and  |-  ( ph  ->  th )

Proof of Theorem mpbi2and
StepHypRef Expression
1 mpbi2and.1 . . 3  |-  ( ph  ->  ps )
2 mpbi2and.2 . . 3  |-  ( ph  ->  ch )
31, 2jca 304 . 2  |-  ( ph  ->  ( ps  /\  ch ) )
4 mpbi2and.3 . 2  |-  ( ph  ->  ( ( ps  /\  ch )  <->  th ) )
53, 4mpbid 146 1  |-  ( ph  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  supisoti  6983  remim  10811  resqrtcl  10980  divalgmod  11873  oddpwdclemxy  12110  divnumden  12137  numdensq  12143  prmdivdiv  12178  4sqlem7  12323  ismgmid2  12621  mnd1  12666  topgele  12780  lmcn2  13033
  Copyright terms: Public domain W3C validator