Theorem stoic1a

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.)

Hypothesis
stoic1.1
\( \vdash \varphi \wedge \psi \rightarrow \theta \)
Conclusion
\( \vdash \varphi \wedge \neg \theta \rightarrow \neg \psi \)
Proof
stoic1.1
ex _
con3dimp _