If every other market balances, the last one must too, Walras proved
Leon Walras showed in 1874 that across an economy's interlocking markets, the total value of everything people want to buy minus everything they want to sell always nets to zero, since every planned purchase is funded by some planned sale. One consequence: if every market but one clears, that last market must clear too. The identity became a basic building block for proving a full set of market-clearing prices can even exist.