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Reyes has allowed one run in 6.2 innings in four appearances at Louisville. He started the season in Pensacola (Double-A).
The 25-year-old native of the Dominican Republic spent a day with the Reds earlier this season but did not get into a game, so he is still awaiting his big-league debut.
Five Reds have already seen their first MLB action this season: Alex Blandino, Tanner Rainey, Zach Weiss, Rosell Herrera and Brandon Dixon.
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Mahle is 7-9 on the season with a 4.95, but he’s been hit hard lately.
In his last seven games, the 23-year-old righty is 1-3 with an 8.04 ERA. He has pitched only 28 innings in that span and given up 25 earned runs on 40 hits and 18 walks and 29 strikeouts.
The Reds had been using a six-man rotation since the All-Star Break.