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Theorem syl6d 69
Description: A nested syllogism deduction. (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 25 . 2  |-  ( ph  ->  ( ps  ->  ( th  ->  ta ) ) )
41, 3syldd 66 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  70  sbi1  2134  omlimcl  7245  ltexprlem7  9437  axpre-sup  9563  caubnd  13202  ubthlem1  25912  ee13  33374  ssralv2  33402  rspsbc2  33406  truniALT  33413
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