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Theorem syl6d 64
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 22 . 2  |-  ( ph  ->  ( ps  ->  ( th  ->  ta ) ) )
41, 3syldd 61 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  syl8  65  cbv1h  1918  sbi1  2003  omlimcl  6576  ltexprlem7  8666  axpre-sup  8791  fzm1  10862  caubnd  11842  ubthlem1  21449  ee13  28265  ssralv2  28294  rspsbc2  28297  truniALT  28305
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
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