It looks like this may be an invalid by-law, when viewed from the “Cooper” case standpoint. But there are other factors that may be relevant, such as the building’s power supply, or its design and any relevant development application conditions. The easiest and cheapest way of challenging this, may be to assemble all the facts, and then arrange for a legal opinion, from an experienced strata lawyer. If there are other owners in the building interested in getting A/C then share the cost. Then send the opinion to the strata committee, together with an application to install the A/C, assuming the opinion favours you.