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Theorem stoic4a 1742
Description: Stoic logic Thema 4 version a. Statement T4 of [Bobzien] p. 117 shows a reconstructed version of Stoic logic Thema 4: "When from two assertibles a third follows, and from the third and one (or both) of the two and one (or more) external assertible(s) another follows, then this other follows from the first two and the external(s)."

We use 𝜃 to represent the "external" assertibles. This is version a, which is without the phrase "or both"; see stoic4b 1743 for the version with the phrase "or both". (Contributed by David A. Wheeler, 17-Feb-2019.)

Hypotheses
Ref Expression
stoic4a.1 ((𝜑𝜓) → 𝜒)
stoic4a.2 ((𝜒𝜑𝜃) → 𝜏)
Assertion
Ref Expression
stoic4a ((𝜑𝜓𝜃) → 𝜏)

Proof of Theorem stoic4a
StepHypRef Expression
1 stoic4a.1 . . 3 ((𝜑𝜓) → 𝜒)
213adant3 1101 . 2 ((𝜑𝜓𝜃) → 𝜒)
3 simp1 1081 . 2 ((𝜑𝜓𝜃) → 𝜑)
4 simp3 1083 . 2 ((𝜑𝜓𝜃) → 𝜃)
5 stoic4a.2 . 2 ((𝜒𝜑𝜃) → 𝜏)
62, 3, 4, 5syl3anc 1366 1 ((𝜑𝜓𝜃) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  w3a 1054
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-an 385  df-3an 1056
This theorem is referenced by: (None)
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