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Theorem syl6d 73
 Description: A nested syllogism deduction. Deduction associated with syl6 34. (Contributed by NM, 11-May-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.) (Proof shortened by Mel L. O'Cat, 2-Feb-2006.)
Hypotheses
Ref Expression
syl6d.1 (𝜑 → (𝜓 → (𝜒𝜃)))
syl6d.2 (𝜑 → (𝜃𝜏))
Assertion
Ref Expression
syl6d (𝜑 → (𝜓 → (𝜒𝜏)))

Proof of Theorem syl6d
StepHypRef Expression
1 syl6d.1 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
2 syl6d.2 . . 3 (𝜑 → (𝜃𝜏))
32a1d 25 . 2 (𝜑 → (𝜓 → (𝜃𝜏)))
41, 3syldd 70 1 (𝜑 → (𝜓 → (𝜒𝜏)))
 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:  syl8  74  sbi1  2380  omlimcl  7545  ltexprlem7  9743  axpre-sup  9869  caubnd  13946  ubthlem1  27110  poimirlem29  32608  ee13  37731  ssralv2  37758  rspsbc2  37765  truniALT  37772  stgoldbwt  40198
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