MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp221 Unicode version

Theorem simp221 1096
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp221  |-  ( ( et  /\  ( th 
/\  ( ph  /\  ps  /\  ch )  /\  ta )  /\  ze )  ->  ph )

Proof of Theorem simp221
StepHypRef Expression
1 simp21 988 . 2  |-  ( ( th  /\  ( ph  /\ 
ps  /\  ch )  /\  ta )  ->  ph )
213ad2ant2 977 1  |-  ( ( et  /\  ( th 
/\  ( ph  /\  ps  /\  ch )  /\  ta )  /\  ze )  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 934
This theorem is referenced by:  4atexlemcnd  30261  cdleme26eALTN  30550  cdleme27a  30556  cdlemk23-3  31091  cdlemk25-3  31093  cdlemk27-3  31096
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 177  df-an 360  df-3an 936
  Copyright terms: Public domain W3C validator