Theorem orcs

Deduction eliminating disjunct. Notational convention: We sometimes suffix with "s" the label of an inference that manipulates an antecedent, leaving the consequent unchanged. The "s" means that the inference eliminates the need for a syllogism ( syl) -type inference in a proof. (Contributed by NM, 21-Jun-1994.)

Hypothesis
orcs.1
\( \vdash \varphi \vee \psi \rightarrow \chi \)
Conclusion
\( \vdash \varphi \rightarrow \chi \)
Proof
l0
orc
\( \vdash \varphi \rightarrow \varphi \vee \psi \)
orcs.1
\( \vdash \varphi \vee \psi \rightarrow \chi \)
syl l0 _