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Theorem stoic3 1411
 Description: Stoic logic Thema 3. Statement T3 of [Bobzien] p. 116-117 discusses Stoic logic thema 3. "When from two (assemblies) a third follows, and from the one that follows (i.e., the third) together with another, external external assumption, another follows, then other follows from the first two and the externally co-assumed one. (Simp. Cael. 237.2-4)" (Contributed by David A. Wheeler, 17-Feb-2019.)
Hypotheses
Ref Expression
stoic3.1 ((𝜑𝜓) → 𝜒)
stoic3.2 ((𝜒𝜃) → 𝜏)
Assertion
Ref Expression
stoic3 ((𝜑𝜓𝜃) → 𝜏)

Proof of Theorem stoic3
StepHypRef Expression
1 stoic3.1 . . 3 ((𝜑𝜓) → 𝜒)
2 stoic3.2 . . 3 ((𝜒𝜃) → 𝜏)
31, 2sylan 281 . 2 (((𝜑𝜓) ∧ 𝜃) → 𝜏)
433impa 1177 1 ((𝜑𝜓𝜃) → 𝜏)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 103   ∧ 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:  f1imaeng  6734  absdiflt  10985  absdifle  10986  xrmaxlesup  11149  fsumdifsnconst  11345  cos01gt0  11652  opnneiss  12529  cxpmul  13204
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