MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp1r3 Structured version   Unicode version

Theorem simp1r3 1094
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp1r3  |-  ( ( ( th  /\  ( ph  /\  ps  /\  ch ) )  /\  ta  /\  et )  ->  ch )

Proof of Theorem simp1r3
StepHypRef Expression
1 simpr3 1004 . 2  |-  ( ( th  /\  ( ph  /\ 
ps  /\  ch )
)  ->  ch )
213ad2ant1 1017 1  |-  ( ( ( th  /\  ( ph  /\  ps  /\  ch ) )  /\  ta  /\  et )  ->  ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    /\ w3a 973
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 975
This theorem is referenced by:  stoweidlem60  31360  lshpkrlem6  33912  atbtwnexOLDN  34243  atbtwnex  34244  3dim3  34265  3atlem5  34283  lplnle  34336  4atlem11  34405  4atexlem7  34871  cdleme22b  35137
  Copyright terms: Public domain W3C validator