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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, 2020
Jun. 30, 2019
Jun. 30, 2020
Jun. 30, 2019
Share-Based Compensation (Textual) [Abstract]        
Pre-tax share-based compensation expense $ 12.3 $ 10.7 $ 34.7 $ 32.5
Stock options        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     973 961
Wtd. Avg. Share Fair Value (usd per share)     $ 35.79 $ 32.48
Performance shares        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     37 57
Wtd. Avg. Share Fair Value (usd per share)     $ 265.04 $ 155.04
Restricted stock and restricted stock units        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     67 46
Wtd. Avg. Share Fair Value (usd per share)     $ 198.77 $ 170.79
Unrestricted stock        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     7 6
Wtd. Avg. Share Fair Value (usd per share)     $ 171.51 $ 182.88