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Theorem syl6d 71
Description: A nested syllogism deduction. Deduction associated with syl6 34. (Contributed by NM, 11-May-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.) (Proof shortened by Mel L. 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 26 . 2  |-  ( ph  ->  ( ps  ->  ( th  ->  ta ) ) )
41, 3syldd 68 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  syl8  72  sbi1  2231  omlimcl  7304  ltexprlem7  9492  axpre-sup  9618  caubnd  13469  ubthlem1  26560  poimirlem29  32013  ee13  36903  ssralv2  36931  rspsbc2  36938  truniALT  36945  stgoldbwt  38914
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