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Theorem syldd 65
Description: Nested syllogism deduction. (Contributed by NM, 12-Dec-2004.) (Proof shortened by Wolf Lammen, 11-May-2013.)
Hypotheses
Ref Expression
syldd.1 (𝜑 → (𝜓 → (𝜒𝜃)))
syldd.2 (𝜑 → (𝜓 → (𝜃𝜏)))
Assertion
Ref Expression
syldd (𝜑 → (𝜓 → (𝜒𝜏)))

Proof of Theorem syldd
StepHypRef Expression
1 syldd.2 . 2 (𝜑 → (𝜓 → (𝜃𝜏)))
2 syldd.1 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
3 imim2 53 . 2 ((𝜃𝜏) → ((𝜒𝜃) → (𝜒𝜏)))
41, 2, 3syl6c 64 1 (𝜑 → (𝜓 → (𝜒𝜏)))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  syl5d  66  syl6d  68  syl10  1340  ordiso2  6415
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