We investigate the connection between optimal propositional
proof systems and complete languages for promise classes.
We prove that an optimal propositional proof system exists
if and only if there exists a propositional proof system
in which every promise class with the test set in co-NP
is representable. Additionally, we prove that there exists
a complete language for UP if and only if there exists
a propositional proof system such that UP is representable
in it. UP is the standard promise class with the test set
in co-NP.