MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp113 Structured version   Unicode version

Theorem simp113 1128
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp113  |-  ( ( ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta )  /\  et  /\  ze )  ->  ch )

Proof of Theorem simp113
StepHypRef Expression
1 simp13 1029 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ch )
213ad2ant1 1018 1  |-  ( ( ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta )  /\  et  /\  ze )  ->  ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ w3a 974
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 369  df-3an 976
This theorem is referenced by:  axcontlem4  24674  llncvrlpln2  32554  4atlem12b  32608  2lnat  32781  cdlemblem  32790  4atexlemex6  33071  cdleme24  33351  cdleme26ee  33359  cdlemg2idN  33595  dihglblem2N  34294  0ellimcdiv  37004  limclner  37006
  Copyright terms: Public domain W3C validator