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Share-Based Compensation (Details) - USD ($)
$ / shares in Units, shares in Thousands, $ in Millions
3 Months Ended 9 Months Ended
Jun. 30, 2019
Jun. 30, 2018
Jun. 30, 2019
Jun. 30, 2018
Share-Based Compensation (Textual) [Abstract]        
Pre-tax share-based compensation expense $ 10.7 $ 9.9 $ 32.5 $ 28.6
Stock options        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     961 865
Wtd. Avg. Share Fair Value (usd per share)     $ 32.48 $ 35.46
Performance shares        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     57 40
Wtd. Avg. Share Fair Value (usd per share)     $ 155.04 $ 219.04
Restricted stock and restricted stock units        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     46 45
Wtd. Avg. Share Fair Value (usd per share)     $ 170.79 $ 188.98
Unrestricted stock        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     6 7
Wtd. Avg. Share Fair Value (usd per share)     $ 182.88 $ 183.76