MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simpr13 Unicode version

Theorem simpr13 1043
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simpr13  |-  ( ( et  /\  ( (
ph  /\  ps  /\  ch )  /\  th  /\  ta ) )  ->  ch )

Proof of Theorem simpr13
StepHypRef Expression
1 simp13 989 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ch )
21adantl 453 1  |-  ( ( et  /\  ( (
ph  /\  ps  /\  ch )  /\  th  /\  ta ) )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359    /\ w3a 936
This theorem is referenced by:  cgr3tr4  25898  btwnoutside  25971  paddasslem8  30321  cdleme27a  30861
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