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Theorem syl5d 67
Description: A nested syllogism deduction. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.) (Proof shortened by O'Cat, 2-Feb-2006.)
Hypotheses
Ref Expression
syl5d.1 (𝜑 → (𝜓𝜒))
syl5d.2 (𝜑 → (𝜃 → (𝜒𝜏)))
Assertion
Ref Expression
syl5d (𝜑 → (𝜃 → (𝜓𝜏)))

Proof of Theorem syl5d
StepHypRef Expression
1 syl5d.1 . . 3 (𝜑 → (𝜓𝜒))
21a1d 22 . 2 (𝜑 → (𝜃 → (𝜓𝜒)))
3 syl5d.2 . 2 (𝜑 → (𝜃 → (𝜒𝜏)))
42, 3syldd 66 1 (𝜑 → (𝜃 → (𝜓𝜏)))
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:  syl7  68  syl9  71  imim12d  73  jaddc  795  pm4.79dc  843
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