ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simpl3r Unicode version

Theorem simpl3r 1038
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simpl3r  |-  ( ( ( ch  /\  th  /\  ( ph  /\  ps ) )  /\  ta )  ->  ps )

Proof of Theorem simpl3r
StepHypRef Expression
1 simp3r 1011 . 2  |-  ( ( ch  /\  th  /\  ( ph  /\  ps )
)  ->  ps )
21adantr 274 1  |-  ( ( ( ch  /\  th  /\  ( ph  /\  ps ) )  /\  ta )  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 963
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 965
This theorem is referenced by:  tfisi  4508  ltmul1a  8376  lemul1a  8639  xrbdtri  11076  dvdscmulr  11556  dvdsmulcr  11557  dvdsadd2b  11574
  Copyright terms: Public domain W3C validator