ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3anandirs Unicode version

Theorem 3anandirs 1238
Description: Inference that undistributes a triple conjunction in the antecedent. (Contributed by NM, 25-Jul-2006.) (Revised by NM, 18-Apr-2007.)
Hypothesis
Ref Expression
3anandirs.1  |-  ( ( ( ph  /\  th )  /\  ( ps  /\  th )  /\  ( ch 
/\  th ) )  ->  ta )
Assertion
Ref Expression
3anandirs  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ta )

Proof of Theorem 3anandirs
StepHypRef Expression
1 simpl1 907 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ph )
2 simpr 103 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  th )
3 simpl2 908 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ps )
4 simpl3 909 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ch )
5 3anandirs.1 . 2  |-  ( ( ( ph  /\  th )  /\  ( ps  /\  th )  /\  ( ch 
/\  th ) )  ->  ta )
61, 2, 3, 2, 4, 2, 5syl222anc 1151 1  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 97    /\ w3a 885
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 887
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator