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Investments in Nonconsolidated Affiliates Investments in Nonconsolidated Affiliates - Schedule of Equity Method Earnings (Details) - USD ($) $ in Millions	12 Months Ended
	Jun. 02, 2018	Jun. 03, 2017	May 28, 2016
Equity Method Investments and Joint Ventures [Abstract]
Equity earnings from nonconsolidated affiliates, net of tax	$ 3.0	$ 1.6	$ 0.4

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This item represents the entity's proportionate share for the period of the net income (loss) of its investee (such as unconsolidated subsidiaries and joint ventures) to which the equity method of accounting is applied. This item includes income or expense related to stock-based compensation based on the investor's grant of stock to employees of an equity method investee.

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