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Theorem syl5d 69
Description: A nested syllogism deduction. Deduction associated with syl5 33. (Contributed by NM, 14-May-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.) (Proof shortened by Mel L. O'Cat, 2-Feb-2006.)
Hypotheses
Ref Expression
syl5d.1  |-  ( ph  ->  ( ps  ->  ch ) )
syl5d.2  |-  ( ph  ->  ( th  ->  ( ch  ->  ta ) ) )
Assertion
Ref Expression
syl5d  |-  ( ph  ->  ( th  ->  ( ps  ->  ta ) ) )

Proof of Theorem syl5d
StepHypRef Expression
1 syl5d.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21a1d 26 . 2  |-  ( ph  ->  ( th  ->  ( ps  ->  ch ) ) )
3 syl5d.2 . 2  |-  ( ph  ->  ( th  ->  ( ch  ->  ta ) ) )
42, 3syldd 68 1  |-  ( ph  ->  ( th  ->  ( ps  ->  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:  syl7  70  syl9  73  imim12d  77  sbi1  2190  mopick  2334  isofrlem  6246  kmlem9  8595  squeeze0  10516  lcmfunsnlem1  14609  fgss2  20887  ordcmp  31112  linepsubN  33286  pmapsub  33302  bgoldbnnsum3prm  38769
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