Will I lose my thermostat settings if I replace the batteries?

All settings other than time and day are permanently stored in memory and do not require battery power to be retained. If batteries are inserted within two minutes of removal, the time and day will not need to be reset either. (Page 11)

From the official Honeywell T4 Pro Programmable Thermostat (TH4110U2005/U) manual, page 11

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