Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  stoic3 GIF version

Theorem stoic3 1320
 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 267 . 2 (((𝜑𝜓) ∧ 𝜃) → 𝜏)
433impa 1099 1 ((𝜑𝜓𝜃) → 𝜏)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ∧ w3a 885 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101 This theorem depends on definitions:  df-bi 110  df-3an 887 This theorem is referenced by:  f1imaeng  6272  absdiflt  9688  absdifle  9689
 Copyright terms: Public domain W3C validator