MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp313 Structured version   Unicode version

Theorem simp313 1137
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp313  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ch )

Proof of Theorem simp313
StepHypRef Expression
1 simp13 1020 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ch )
213ad2ant3 1011 1  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ w3a 965
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 967
This theorem is referenced by:  dalemrot  33298  dalem5  33308  dalem-cly  33312  dath2  33378  cdleme26e  34000  cdleme38m  34104  cdleme38n  34105  cdlemg28b  34344  cdlemg28  34345  cdlemk7  34489  cdlemk11  34490  cdlemk12  34491  cdlemk7u  34511  cdlemk11u  34512  cdlemk12u  34513  cdlemk22  34534  cdlemk23-3  34543  cdlemk25-3  34545
  Copyright terms: Public domain W3C validator