MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp3r1 Structured version   Unicode version

Theorem simp3r1 1066
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp3r1  |-  ( ( ta  /\  et  /\  ( th  /\  ( ph  /\ 
ps  /\  ch )
) )  ->  ph )

Proof of Theorem simp3r1
StepHypRef Expression
1 simpr1 964 . 2  |-  ( ( th  /\  ( ph  /\ 
ps  /\  ch )
)  ->  ph )
213ad2ant3 981 1  |-  ( ( ta  /\  et  /\  ( th  /\  ( ph  /\ 
ps  /\  ch )
) )  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360    /\ w3a 937
This theorem is referenced by:  nllyrest  17551  segletr  26050  stoweidlem56  27783  cdlemblem  30652  cdleme21  31196  cdleme22b  31200  cdleme40m  31326  cdlemg34  31571  cdlemk5u  31720  cdlemk6u  31721  cdlemk21N  31732  cdlemk20  31733  cdlemk26b-3  31764  cdlemk26-3  31765  cdlemk28-3  31767  cdlemk37  31773  cdlemky  31785  cdlemk11t  31805  cdlemkyyN  31821  dihmeetlem20N  32186
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 179  df-an 362  df-3an 939
  Copyright terms: Public domain W3C validator