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 and stoic1b to represent each side. (Contributed by David A. Wheeler, 16-Feb-2019) (Proof shortened by Wolf Lammen, 21-May-2020)
Ref | Expression | ||
---|---|---|---|
Hypothesis | stoic1.1 | |- ( ( ph /\ ps ) -> th ) |
|
Assertion | stoic1a | |- ( ( ph /\ -. th ) -> -. ps ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | stoic1.1 | |- ( ( ph /\ ps ) -> th ) |
|
2 | 1 | ex | |- ( ph -> ( ps -> th ) ) |
3 | 2 | con3dimp | |- ( ( ph /\ -. th ) -> -. ps ) |