MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp111 Structured version   Unicode version

Theorem simp111 1134
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp111  |-  ( ( ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta )  /\  et  /\  ze )  ->  ph )

Proof of Theorem simp111
StepHypRef Expression
1 simp11 1035 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ph )
213ad2ant1 1026 1  |-  ( ( ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta )  /\  et  /\  ze )  ->  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ w3a 982
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 188  df-an 372  df-3an 984
This theorem is referenced by:  tsmsxp  21100  ps-2b  32756  llncvrlpln2  32831  4atlem11b  32882  4atlem12b  32885  lplncvrlvol2  32889  lneq2at  33052  2lnat  33058  cdlemblem  33067  4atexlemex6  33348  cdleme24  33628  cdleme26ee  33636  cdlemg2idN  33872  cdlemg31c  33975  cdlemk26-3  34182  0ellimcdiv  37302
  Copyright terms: Public domain W3C validator