MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp1l3 Structured version   Unicode version

Theorem simp1l3 1091
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp1l3  |-  ( ( ( ( ph  /\  ps  /\  ch )  /\  th )  /\  ta  /\  et )  ->  ch )

Proof of Theorem simp1l3
StepHypRef Expression
1 simpl3 1001 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ch )
213ad2ant1 1017 1  |-  ( ( ( ( ph  /\  ps  /\  ch )  /\  th )  /\  ta  /\  et )  ->  ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    /\ w3a 973
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 371  df-3an 975
This theorem is referenced by:  btwnconn1lem7  29317  btwnconn1lem12  29322  linethru  29377  hlrelat3  34208  cvrval3  34209  2atlt  34235  atbtwnex  34244  1cvratlt  34270  2llnmat  34320  lplnexllnN  34360  4atlem11  34405  lnjatN  34576  lncvrat  34578  lncmp  34579  cdlemd9  35002  dihord5b  36056  dihmeetALTN  36124  dih1dimatlem0  36125  mapdrvallem2  36442
  Copyright terms: Public domain W3C validator