MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp321 Unicode version

Theorem simp321 1107
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp321  |-  ( ( et  /\  ze  /\  ( th  /\  ( ph  /\ 
ps  /\  ch )  /\  ta ) )  ->  ph )

Proof of Theorem simp321
StepHypRef Expression
1 simp21 990 . 2  |-  ( ( th  /\  ( ph  /\ 
ps  /\  ch )  /\  ta )  ->  ph )
213ad2ant3 980 1  |-  ( ( et  /\  ze  /\  ( th  /\  ( ph  /\ 
ps  /\  ch )  /\  ta ) )  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 936
This theorem is referenced by:  dalemcnes  30286  dalempnes  30287  dalemrot  30293  dath2  30373  cdleme18d  30931  cdleme20i  30953  cdleme20j  30954  cdleme20l2  30957  cdleme20l  30958  cdleme20m  30959  cdleme20  30960  cdleme21j  30972  cdleme22eALTN  30981  cdlemk16a  31492  cdlemk12u-2N  31526  cdlemk21-2N  31527  cdlemk22  31529  cdlemk31  31532  cdlemk32  31533  cdlemk11ta  31565  cdlemk11tc  31581
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 178  df-an 361  df-3an 938
  Copyright terms: Public domain W3C validator