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Theorem syld3an1 1216
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 1144 . . 3 ((𝜃𝜓𝜒) → 𝜑)
3 syld3an1.2 . . . 4 ((𝜑𝜓𝜃) → 𝜏)
433com13 1144 . . 3 ((𝜃𝜓𝜑) → 𝜏)
52, 4syld3an3 1215 . 2 ((𝜃𝜓𝜒) → 𝜏)
653com13 1144 1 ((𝜒𝜓𝜃) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by:  tfrcllembacc  6050  npncan  7604  nnpcan  7606  ppncan  7625  muldivdirap  8070  div2negap  8098  ltmuldiv  8227  mulqmod0  9624
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