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Theorem stoic4a 1362
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 1363 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 959 . 2 ((𝜑𝜓𝜃) → 𝜒)
3 simp1 939 . 2 ((𝜑𝜓𝜃) → 𝜑)
4 simp3 941 . 2 ((𝜑𝜓𝜃) → 𝜃)
5 stoic4a.2 . 2 ((𝜒𝜑𝜃) → 𝜏)
62, 3, 4, 5syl3anc 1170 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: (None)
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