"If you break it, it will explode."
Another example where adding vaj after chugh is incorrect. If you break it, then it will explode should be acceptable,no?
In English, the sentence works well either with or without "then". In Klingon the sentence works well either with or without vaj. Since there is such a nice correlation between the two, we ask you to match them in your translations. When either "then" or vaj are present in the original sentence we ask you to include the other in your translation. When they are absent, then you should not use them in the translations either. In casual conversation, it probably wouldn't matter whether you included it or not, but for learning and translation purposes, we ask that you be consistent in matching them.
I object to this requirement. Good translation is never this rigid, and Okrand himself doesn't follow this rule.
bIjeghbe'chugh vaj bIHegh Surrender or die. (TKD)
bIje'be'chugh vaj bIHegh Buy or die. (CK)
bIDIlbe'chugh vaj bIHegh Pay or die. (PK)
naDev juHlIjDaq cha'logh vISopneSchugh, vaj jIquv. It would be an honor to eat twice here at your house, your honor. (PK)
vaj loghDaq lenglaHtaH Humanpu' ...that mark the continuation of the human adventure into space... (Skybox 99)
qorDu' lurDechmeyna' pab tlhInganpu'. qorDu' SaHlu'chugh 'ej matlhlu'chugh vaj wa' tlhIngan ghob potlhqu'. With strong family traditions, devotion and loyalty to family is one of the most important Klingon virtues. (Skybox S13)
Dumer DIvI' QaS 'ej DuHIv, vaj bIwunchoH 'ej bIrIQchoH. Surprise attack by Federation leaves you unprotected and damaged. (Klingon Monopoly)
(and I haven't even gone looking through paq'batlh.)
None of these sentences have any kind of then, thus, or so in them, but they're perfectly good translations. This has nothing to do with how formal the language is. "For learning and translation purposes," it would be best to teach good translation practices, like not to treat translation like an exercise in word-substitution. To quote a famous Klingonist, "Klingon is not a code for English."