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Theorem syl8ib 165
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 119 . 2  |-  ( th 
->  ta )
41, 3syl8 71 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  pm3.2an3  1145  necon4bddc  2356  necon4abiddc  2358  necon4bbiddc  2359  necon4biddc  2360
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