ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simpl3l Unicode version

Theorem simpl3l 959
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simpl3l  |-  ( ( ( ch  /\  th  /\  ( ph  /\  ps ) )  /\  ta )  ->  ph )

Proof of Theorem simpl3l
StepHypRef Expression
1 simp3l 932 . 2  |-  ( ( ch  /\  th  /\  ( ph  /\  ps )
)  ->  ph )
21adantr 261 1  |-  ( ( ( ch  /\  th  /\  ( ph  /\  ps ) )  /\  ta )  ->  ph )
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:  tfisi  4310  ltmul1a  7582  ltmul1  7583  lemul1a  7824
  Copyright terms: Public domain W3C validator