ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  jca31 Unicode version

Theorem jca31 296
Description: Join three consequents. (Contributed by Jeff Hankins, 1-Aug-2009.)
Hypotheses
Ref Expression
jca31.1  |-  ( ph  ->  ps )
jca31.2  |-  ( ph  ->  ch )
jca31.3  |-  ( ph  ->  th )
Assertion
Ref Expression
jca31  |-  ( ph  ->  ( ( ps  /\  ch )  /\  th )
)

Proof of Theorem jca31
StepHypRef Expression
1 jca31.1 . . 3  |-  ( ph  ->  ps )
2 jca31.2 . . 3  |-  ( ph  ->  ch )
31, 2jca 294 . 2  |-  ( ph  ->  ( ps  /\  ch ) )
4 jca31.3 . 2  |-  ( ph  ->  th )
53, 4jca 294 1  |-  ( ph  ->  ( ( ps  /\  ch )  /\  th )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 105
This theorem is referenced by:  3jca  1095  syl21anc  1145  f1oiso2  5494  nnnq0lem1  6602  prmuloc  6722  prsrlem1  6885  apreap  7652  lemulge11  7907  elnnz  8312  leexp1a  9475  faclbnd6  9612  oddpwdclemdc  10261
  Copyright terms: Public domain W3C validator