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Theorem syl5d 68
Description: A nested syllogism deduction. Deduction associated with syl5 32. (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 25 . 2  |-  ( ph  ->  ( th  ->  ( ps  ->  ch ) ) )
3 syl5d.2 . 2  |-  ( ph  ->  ( th  ->  ( ch  ->  ta ) ) )
42, 3syldd 67 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  69  syl9  72  imim12d  76  sbi1  2241  mopick  2384  isofrlem  6249  kmlem9  8606  squeeze0  10531  lcmfunsnlem1  14689  fgss2  20967  ordcmp  31178  linepsubN  33388  pmapsub  33404  bgoldbnnsum3prm  39044
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