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Theorem syl8ib 222
Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise. (Contributed by NM, 1-Aug-1994.)
Hypotheses
Ref Expression
syl8ib.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
syl8ib.2  |-  ( th  <->  ta )
Assertion
Ref Expression
syl8ib  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )

Proof of Theorem syl8ib
StepHypRef Expression
1 syl8ib.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
2 syl8ib.2 . . 3  |-  ( th  <->  ta )
32biimpi 186 . 2  |-  ( th 
->  ta )
41, 3syl8 65 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176
This theorem is referenced by:  pm3.2an3  1131  en3lplem2  7417  axdc4lem  8081
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
  Copyright terms: Public domain W3C validator