MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp312 Structured version   Unicode version

Theorem simp312 1131
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp312  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ps )

Proof of Theorem simp312
StepHypRef Expression
1 simp12 1014 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ps )
213ad2ant3 1006 1  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ w3a 960
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 962
This theorem is referenced by:  dalemrot  32989  dalem-cly  33003  dath2  33069  cdleme26e  33691  cdleme38m  33795  cdleme38n  33796  cdleme39n  33798  cdlemg28b  34035  cdlemk7  34180  cdlemk11  34181  cdlemk12  34182  cdlemk7u  34202  cdlemk11u  34203  cdlemk12u  34204  cdlemk22  34225  cdlemk23-3  34234  cdlemk25-3  34236
  Copyright terms: Public domain W3C validator