Theorem stoic2a

Stoic logic Thema 2 version a. Statement T2 of [Bobzien] p. 117 shows a reconstructed version of Stoic logic thema 2 as follows: "When from two assertibles a third follows, and from the third and one (or both) of the two another follows, then this other follows from the first two." Bobzien uses constructs such as ph , ps |- ch; in Metamath we will represent that construct as ph /\ ps -> ch. This version a is without the phrase "or both"; see stoic2b for the version with the phrase "or both". We already have this rule as syldan, so here we show the equivalence and discourage its use. (New usage is discouraged.) (Contributed by David A. Wheeler, 17-Feb-2019.)

Hypotheses
stoic2a.1
\( \vdash \varphi \wedge \psi \rightarrow \chi \)
stoic2a.2
\( \vdash \varphi \wedge \chi \rightarrow \theta \)
Conclusion
\( \vdash \varphi \wedge \psi \rightarrow \theta \)
Proof
l0
stoic2a.1
\( \vdash \varphi \wedge \psi \rightarrow \chi \)
stoic2a.2
\( \vdash \varphi \wedge \chi \rightarrow \theta \)
syldan l0 _