MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp3l1 Structured version   Unicode version

Theorem simp3l1 1100
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp3l1  |-  ( ( ta  /\  et  /\  ( ( ph  /\  ps  /\  ch )  /\  th ) )  ->  ph )

Proof of Theorem simp3l1
StepHypRef Expression
1 simpl1 998 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ph )
213ad2ant3 1018 1  |-  ( ( ta  /\  et  /\  ( ( ph  /\  ps  /\  ch )  /\  th ) )  ->  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    /\ w3a 972
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 974
This theorem is referenced by:  cvmlift2lem10  28627  cdleme26ee  35809  cdleme36m  35910  cdleme40m  35916  cdlemg18b  36128  cdlemk5u  36310  cdlemk6u  36311  cdlemk21N  36322  cdlemk20  36323  cdlemk27-3  36356  cdlemk28-3  36357  dihmeetlem20N  36776
  Copyright terms: Public domain W3C validator