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Theorem syl5d 73
Description: A nested syllogism deduction. Deduction associated with syl5 34. (Contributed by NM, 14-May-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.) (Proof shortened by Mel L. 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 25 . 2 (𝜑 → (𝜃 → (𝜓𝜒)))
3 syl5d.2 . 2 (𝜑 → (𝜃 → (𝜒𝜏)))
42, 3syldd 72 1 (𝜑 → (𝜃 → (𝜓𝜏)))
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:  syl7  74  syl9  77  imim12d  81  mopick  2627  isofrlem  7211  kmlem9  9914  squeeze0  11878  lcmfunsnlem1  16342  fgss2  23025  ordcmp  34636  linepsubN  37766  pmapsub  37782  ichreuopeq  44925  bgoldbnnsum3prm  45256
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