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Theorem stoic3 1361
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 277 . 2 (((𝜑𝜓) ∧ 𝜃) → 𝜏)
433impa 1134 1 ((𝜑𝜓𝜃) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  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:  f1imaeng  6439  absdiflt  10352  absdifle  10353
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