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Debt (Narrative) (Details)
€ in Millions, $ in Millions
Dec. 31, 2019
USD ($)
Dec. 31, 2019
EUR (€)
Jun. 30, 2019
USD ($)
Jun. 30, 2019
EUR (€)
Mar. 31, 2000
USD ($)
Senior Notes [Member] | INA Senior Notes Due December 2024 [Member]          
Debt Instrument [Line Items]          
Long-term debt stated interest rate 0.30% 0.30%      
Make Whole Premium Additional Percent 0.15% 0.15%      
Debt Instrument, Face Amount $ 779.0 € 700      
Senior Notes [Member] | INA Senior Notes Due December 2029 [Member]          
Debt Instrument [Line Items]          
Long-term debt stated interest rate 0.875% 0.875%      
Make Whole Premium Additional Percent 0.20% 0.20%      
Debt Instrument, Face Amount $ 779.0 € 700      
Senior Notes [Member] | INA Senior Note Due June 2027 [Member]          
Debt Instrument [Line Items]          
Long-term debt stated interest rate     0.875% 0.875%  
Debt Instrument, Face Amount     $ 650.0 € 575  
Senior Notes [Member] | INA Senior Note Due June 2031 [Member]          
Debt Instrument [Line Items]          
Long-term debt stated interest rate     1.40% 1.40%  
Debt Instrument, Face Amount     $ 650.0 € 575  
Trust Preferred Securities | INA capital securities due 2030          
Debt Instrument [Line Items]          
Long-term debt stated interest rate 9.70% 9.70%     9.70%
ACE Capital Trust II common securities purchased         $ 9.2
Debt Instrument, Face Amount $ 309.0       $ 300.0
Senior Notes [Member] | INA Senior Notes Due June 2019 [Member]          
Debt Instrument [Line Items]          
Long-term debt stated interest rate 5.90% 5.90% 5.90% 5.90%  
Debt Instrument, Face Amount $ 500.0   $ 500.0