I've been getting a lot of pressure to post some Greek syntax rules, so following up on last week's Latin Proviso, I give you the much simpler Greek equivalent.
Interestingly Goodwin refuses to use the term 'proviso' and classes this as a type of consecutive clause, though one could just as easily make the case that a proviso is analogous (in sense though not form) to conditionals. Perhaps understanding this potential overlap Smyth gives the proviso its own place, sandwiched between result clauses and conditionals:
CLAUSES WITH ἐφ' ᾧ AND ἐφ' ᾧτε INTRODUCING A PROVISO
§2279. ἐφ' ᾧ and ἐφ' ᾧτε on condition that, for the purpose of take the infinitive or (less often) the future indicative, and may be introduced, in the principal clause, by the demonstrative ἐπὶ τούτῳ. Negative μή.
αἱρεθέντες ἐφ' ᾧτε συγγράψαι νόμους having been chosen for the purpose of compiling laws X. H. 2.3.11 , ἔφασαν ἀποδώσειν (τοὺς νεκροὺς) ἐφ' ᾧ μὴ καίειν τὰ̄ς οἰκίᾱς the barbarians said they would surrender the dead on condition that he would not burn their houses X. A. 4.2.19, ἀφί̄εμέν σε, ἐπὶ τούτῳ μέντοι, ἐφ' ᾧτε μηκέτι . . . φιλοσοφεῖν we release you, on this condition however, that you no longer search after wisdom P. A. 29c . Future indicative: ξυνέβησαν ἐφ' ᾧτε ἐξίᾱσιν ἐκ Πελοποννήσου ὑπόσπονδοι καὶ μηδέποτε ἐπιβήσονται αὐτῆς they made an agreement on condition that they should depart from the Peloponnesus under a truce and never set foot on it again T. 1.103.
a. These constructions do not occur in Homer. The future indicative is used by Herodotus and Thucydides on the analogy of relative clauses equivalent to consecutive clauses. These authors also use ἐπὶ τοῖσδε for ἐπὶ τούτῳ.