Complex sentence: When the CIO later adopted a wartime no-strike pledge, Bridges supported the pledge and proposed at the highpoint of the Communist Party's enthusiasm for unity--immediately after the Teheran Conference in 1943--that the pledge continue after the end of the war.
Split into simpler sentences: When the CIO later adopted a wartime no-strike pledge, Bridges supported the pledge. He proposed at the highpoint of the Communist Party's enthusiasm for unity--immediately after the Teheran Conference in 1943--that the pledge continue after the end of the war.