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Income Taxes - Components of Income Tax Expense (Benefit) (Details) - USD ($) $ in Millions | 12 Months Ended
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Jun. 01, 2019 | Jun. 02, 2018 | Jun. 03, 2017
Income Tax Disclosure [Abstract] |  |  |
Current: Domestic - Federal | $ 19.0 | $ 30.2 | $ 28.7
Domestic - State | 6.4 | 4.3 | 2.3
Foreign | 12.9 | 10.7 | 11.1
Current Income Tax Expense (Benefit) | 38.3 | 45.2 | 42.1
Deferred: Domestic - Federal | 1.0 | (4.1) | 9.2
Domestic - State | (0.2) | 0.1 | 2.8
Foreign | 0.5 | 1.2 | 1.0
Deferred Income Tax Expense (Benefit) | 1.3 | (2.8) | 13.0
Income tax expense | $ 39.6 | $ 42.4 | $ 55.1

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