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Theorem syldd 68
Description: Nested syllogism deduction. Deduction associated with syld 45. Double deduction associated with syl 17. (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 55 . 2  |-  ( ( th  ->  ta )  ->  ( ( ch  ->  th )  ->  ( ch  ->  ta ) ) )
41, 2, 3syl6c 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:  syl5d  69  syl6d  71  syl10  75  tfinds  6700  tz7.49  7170  dffi2  7943  ordiso2  8030  rankuni2b  8323  brbtwn2  24781  soseq  30279  prtlem60  32121  lvoli2  32855
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