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First Trust Small Cap Value AlphaDEX Fund Average Annual Total Returns
 12 Months Ended 60 Months Ended 120 Months Ended 164 Months Ended 212 Months Ended
Jul. 31, 2025
Dec. 31, 2024
Dec. 31, 2024
Dec. 31, 2024
Dec. 31, 2024
Dec. 31, 2024
Nasdaq AlphaDEX Small Cap Value(TM) Index (reflects no deduction for fees, expenses or taxes)[Member]            
Prospectus [Line Items]            
Average Annual Return, Percent [1]   4.07% 10.09%  
Nasdaq US 700 Small Cap Value(TM) Index (reflects no deduction for fees, expenses or taxes)[Member]            
Prospectus [Line Items]            
Average Annual Return, Percent [1]   6.11% 8.87%  
S&P SmallCap 600® Value Index (reflects no deduction for fees, expenses or taxes)[Member]            
Prospectus [Line Items]            
Average Annual Return, Percent   7.56% 8.10% 8.18% 10.11%  
Russell 3000® Index (reflects no deduction for fees, expenses or taxes)[Member]            
Prospectus [Line Items]            
Average Annual Return, Percent   23.81% 13.86% 12.55% 13.21% 9.93%
First Trust Small Cap Value AlphaDEX Fund            
Prospectus [Line Items]            
Average Annual Return, Percent   3.16% 9.21% 6.79% 9.01%  
Performance Inception Date Apr. 19, 2011          
First Trust Small Cap Value AlphaDEX Fund | After Taxes on Distributions            
Prospectus [Line Items]            
Average Annual Return, Percent   2.29% 8.54% 6.18% 8.46%  
First Trust Small Cap Value AlphaDEX Fund | After Taxes on Distributions and Sales            
Prospectus [Line Items]            
Average Annual Return, Percent   1.86% 6.95% 5.14% 7.24%  
[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.