Users' Mathboxes Mathbox for David A. Wheeler < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  resolution Structured version   Unicode version

Theorem resolution 28611
Description: Resolution rule. This is the primary inference rule in some automated theorem provers such as prover9. The resolution rule can be traced back to Davis and Putnam (1960). (Contributed by David A. Wheeler, 9-Feb-2017.)
Assertion
Ref Expression
resolution  |-  ( ( ( ph  /\  ps )  \/  ( -.  ph 
/\  ch ) )  -> 
( ps  \/  ch ) )

Proof of Theorem resolution
StepHypRef Expression
1 simpr 449 . 2  |-  ( (
ph  /\  ps )  ->  ps )
2 simpr 449 . 2  |-  ( ( -.  ph  /\  ch )  ->  ch )
31, 2orim12i 504 1  |-  ( ( ( ph  /\  ps )  \/  ( -.  ph 
/\  ch ) )  -> 
( ps  \/  ch ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 359    /\ wa 360
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 179  df-or 361  df-an 362
  Copyright terms: Public domain W3C validator