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Theorem syl6d 66
Description: A nested syllogism deduction. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.) (Proof shortened by O'Cat, 2-Feb-2006.)
Hypotheses
Ref Expression
syl6d.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
syl6d.2  |-  ( ph  ->  ( th  ->  ta ) )
Assertion
Ref Expression
syl6d  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )

Proof of Theorem syl6d
StepHypRef Expression
1 syl6d.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
2 syl6d.2 . . 3  |-  ( ph  ->  ( th  ->  ta ) )
32a1d 23 . 2  |-  ( ph  ->  ( ps  ->  ( th  ->  ta ) ) )
41, 3syldd 63 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  syl8  67  cbv1h  2031  sbi1  2112  omlimcl  6780  ltexprlem7  8875  axpre-sup  9000  fzm1  11082  caubnd  12117  ubthlem1  22325  ee13  28297  ssralv2  28326  rspsbc2  28329  truniALT  28337  cbv1hwAUX7  29217  sbi1NEW7  29267  cbv1hOLD7  29403
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
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