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Theorem syldd 66
Description: Nested syllogism deduction. (Contributed by NM, 12-Dec-2004.) (Proof shortened by Wolf Lammen, 11-May-2013.)
Hypotheses
Ref Expression
syldd.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
syldd.2  |-  ( ph  ->  ( ps  ->  ( th  ->  ta ) ) )
Assertion
Ref Expression
syldd  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )

Proof of Theorem syldd
StepHypRef Expression
1 syldd.2 . 2  |-  ( ph  ->  ( ps  ->  ( th  ->  ta ) ) )
2 syldd.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
3 imim2 53 . 2  |-  ( ( th  ->  ta )  ->  ( ( ch  ->  th )  ->  ( ch  ->  ta ) ) )
41, 2, 3syl6c 64 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:  syl5d  67  syl6d  69  syl10  73  tfinds  6470  tz7.49  6900  dffi2  7673  ordiso2  7729  rankuni2b  8060  brbtwn2  23151  soseq  27715  prtlem60  28986  lvoli2  33225
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