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Mirrors > Home > MPE Home > Th. List > stoic1a | Structured version Visualization version GIF version |
Description: Stoic logic Thema 1 (part
a).
The first thema of the four Stoic logic themata, in its basic form, was: "When from two (assertibles) a third follows, then from either of them together with the contradictory of the conclusion the contradictory of the other follows." (Apuleius Int. 209.9-14), see [Bobzien] p. 117 and https://plato.stanford.edu/entries/logic-ancient/ We will represent thema 1 as two very similar rules stoic1a 1775 and stoic1b 1776 to represent each side. (Contributed by David A. Wheeler, 16-Feb-2019.) (Proof shortened by Wolf Lammen, 21-May-2020.) |
Ref | Expression |
---|---|
stoic1.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜃) |
Ref | Expression |
---|---|
stoic1a | ⊢ ((𝜑 ∧ ¬ 𝜃) → ¬ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | stoic1.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜃) | |
2 | 1 | ex 414 | . 2 ⊢ (𝜑 → (𝜓 → 𝜃)) |
3 | 2 | con3dimp 410 | 1 ⊢ ((𝜑 ∧ ¬ 𝜃) → ¬ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 397 |
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 206 df-an 398 |
This theorem is referenced by: stoic1b 1776 posn 5762 frsn 5764 relimasn 6084 nssdmovg 7589 iblss 25322 midexlem 27943 colhp 28021 clwwlknon0 29346 xaddeq0 31966 xrge0npcan 32195 unccur 36471 lindsenlbs 36483 itg2addnclem2 36540 dvasin 36572 ssnel 43727 icccncfext 44603 dirkercncflem1 44819 fourierdlem81 44903 fourierdlem97 44919 prsal 45034 volico2 45357 |
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