MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp311 Structured version   Visualization version   Unicode version

Theorem simp311 1155
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp311  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ph )

Proof of Theorem simp311
StepHypRef Expression
1 simp11 1038 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ph )
213ad2ant3 1031 1  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ w3a 985
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 189  df-an 373  df-3an 987
This theorem is referenced by:  dalem-clpjq  33202  dath2  33302  cdleme26e  33926  cdleme38m  34030  cdleme38n  34031  cdleme39n  34033  cdlemg28b  34270  cdlemk7  34415  cdlemk11  34416  cdlemk12  34417  cdlemk7u  34437  cdlemk11u  34438  cdlemk12u  34439  cdlemk22  34460  cdlemk23-3  34469  cdlemk25-3  34471
  Copyright terms: Public domain W3C validator