MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp322 Structured version   Unicode version

Theorem simp322 1148
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp322  |-  ( ( et  /\  ze  /\  ( th  /\  ( ph  /\ 
ps  /\  ch )  /\  ta ) )  ->  ps )

Proof of Theorem simp322
StepHypRef Expression
1 simp22 1031 . 2  |-  ( ( th  /\  ( ph  /\ 
ps  /\  ch )  /\  ta )  ->  ps )
213ad2ant3 1020 1  |-  ( ( et  /\  ze  /\  ( th  /\  ( ph  /\ 
ps  /\  ch )  /\  ta ) )  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ w3a 974
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 976
This theorem is referenced by:  dalemqnet  35110  dalemrot  35115  dath2  35195  cdleme18d  35754  cdleme20i  35777  cdleme20j  35778  cdleme20l2  35781  cdleme20l  35782  cdleme20m  35783  cdleme20  35784  cdleme21j  35796  cdleme22eALTN  35805  cdleme26eALTN  35821  cdlemk16a  36316  cdlemk12u-2N  36350  cdlemk21-2N  36351  cdlemk22  36353  cdlemk31  36356  cdlemk32  36357  cdlemk11ta  36389  cdlemk11tc  36405
  Copyright terms: Public domain W3C validator