Is it possible to contribute the MAX amount to both a 401k and contribute the MAX to a Traditional IRA and jump down to a lower tax bracket?

Details: Setting up my parents for retirement. Father makes 107k, Mother no income. File Married Joint every year. Fall under 25% tax bracket for 2017, 22% bracket for 2018. If he contributes the Max amount to his 401k (24,500/2018 for 57 and older) and Opens up a Traditional IRA and Maxes it as well. The income subject to Taxes would be below 77k, jumping down to a 12% Bracket in 2018. Taxes go down and Retirement goes up. Playing Catch up. Keeping the same Lifestyle, give or take a couple hundred dollars a month.