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First Trust Large Cap Core AlphaDEX Fund Average Annual Total Returns
 12 Months Ended 60 Months Ended 120 Months Ended 212 Months Ended
Jul. 31, 2025
Dec. 31, 2024
Dec. 31, 2024
Dec. 31, 2024
Dec. 31, 2024
Nasdaq AlphaDEX Large Cap Core(TM) Index (reflects no deduction for fees, expenses or taxes)[Member]          
Prospectus [Line Items]          
Average Annual Return, Percent [1]   17.84% 11.97%
Nasdaq US 500 Large Cap(TM) Index (reflects no deduction for fees, expenses or taxes)[Member]          
Prospectus [Line Items]          
Average Annual Return, Percent [1]   25.61% 14.59%
S&P 500® Index (reflects no deduction for fees, expenses or taxes)[Member]          
Prospectus [Line Items]          
Average Annual Return, Percent   25.02% 14.53% 13.10% 10.17%
First Trust Large Cap Core AlphaDEX Fund          
Prospectus [Line Items]          
Average Annual Return, Percent   17.13% 11.30% 10.06% 8.67%
Performance Inception Date May 08, 2007        
First Trust Large Cap Core AlphaDEX Fund | After Taxes on Distributions          
Prospectus [Line Items]          
Average Annual Return, Percent   16.55% 10.69% 9.46% 8.13%
First Trust Large Cap Core AlphaDEX Fund | After Taxes on Distributions and Sales          
Prospectus [Line Items]          
Average Annual Return, Percent   10.13% 8.68% 7.95% 7.04%
[1] Performance data is not available for all the periods shown in the table for the index because performance data does not exist for some of the entire periods.