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

Theorem simp312 1154
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 1037 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ps )
213ad2ant3 1029 1  |-  ( ( et  /\  ze  /\  ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta ) )  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ w3a 983
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 985
This theorem is referenced by:  dalemrot  33185  dalem-cly  33199  dath2  33265  cdleme26e  33889  cdleme38m  33993  cdleme38n  33994  cdleme39n  33996  cdlemg28b  34233  cdlemk7  34378  cdlemk11  34379  cdlemk12  34380  cdlemk7u  34400  cdlemk11u  34401  cdlemk12u  34402  cdlemk22  34423  cdlemk23-3  34432  cdlemk25-3  34434
  Copyright terms: Public domain W3C validator