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Theorem syld3an1 1266
 Description: A syllogism inference. (Contributed by NM, 7-Jul-2008.)
Hypotheses
Ref Expression
syld3an1.1 ((𝜒𝜓𝜃) → 𝜑)
syld3an1.2 ((𝜑𝜓𝜃) → 𝜏)
Assertion
Ref Expression
syld3an1 ((𝜒𝜓𝜃) → 𝜏)

Proof of Theorem syld3an1
StepHypRef Expression
1 syld3an1.1 . . . 4 ((𝜒𝜓𝜃) → 𝜑)
213com13 1190 . . 3 ((𝜃𝜓𝜒) → 𝜑)
3 syld3an1.2 . . . 4 ((𝜑𝜓𝜃) → 𝜏)
433com13 1190 . . 3 ((𝜃𝜓𝜑) → 𝜏)
52, 4syld3an3 1265 . 2 ((𝜃𝜓𝜒) → 𝜏)
653com13 1190 1 ((𝜒𝜓𝜃) → 𝜏)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ w3a 963 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107 This theorem depends on definitions:  df-bi 116  df-3an 965 This theorem is referenced by:  tfrcllembacc  6296  npncan  8079  nnpcan  8081  ppncan  8100  muldivdirap  8563  div2negap  8591  ltmuldiv  8728  mulqmod0  10211
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