I believe 2nd ed AD&D introduced this rule. In Gygaxian AD&D it applied to thieves - so a multi-classed thief had to wear only leather armour (or the other permitted armour types that UA opened up for thieves) - but not magic-users or cleric - so a F/MU could cast in armour, and a C/F could use edged weapons - with the exception of gnomes, who for some reason as fighter/illusionists were limited to leather armour only.Multi-classing
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if a class was banned from using certain items then it didn't matter that the other was permitted them, so a F/MU usually didn't wear armour.
You needed at least 15 in your old prime requisite(s) and 17 in your knew one(s) to dual-class. This was the main reason why I never saw it in play.Dual classing was available only to human characters.