ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  stoic4a GIF version

Theorem stoic4a 1393
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 1394 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 986 . 2 ((𝜑𝜓𝜃) → 𝜒)
3 simp1 966 . 2 ((𝜑𝜓𝜃) → 𝜑)
4 simp3 968 . 2 ((𝜑𝜓𝜃) → 𝜃)
5 stoic4a.2 . 2 ((𝜒𝜑𝜃) → 𝜏)
62, 3, 4, 5syl3anc 1201 1 ((𝜑𝜓𝜃) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 947
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 949
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator