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Theorem syl6d 75
 Description: A nested syllogism deduction. Deduction associated with syl6 35. (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 72 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  76  sbi1OLD  2536  sbi1ALT  2599  omlimcl  8197  ltexprlem7  10456  axpre-sup  10583  caubnd  14711  ubthlem1  28562  poimirlem29  34789  ee13  40700  ssralv2  40727  rspsbc2  40730  truniALT  40737  stgoldbwt  43770
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