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Theorem syldd 61
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 49 . 2 ((θτ) → ((χθ) → (χτ)))
41, 2, 3syl6c 60 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  62  syl6d  64  syl10  1321
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