I see no prohibitions on such use of the firearm and if you used it to stop threat to life then you would be justified in doing so.
Section 790.06 (12) states " No license issued pursuant to this section shall authorize any person to carry a concealed weapon or firearm into any place of nuisance as defined in s. 823.05; any police, sheriff, or highway patrol station; any detention facility, prison, or jail; any courthouse; any courtroom, except that nothing in this section would preclude a judge from carrying a concealed weapon or determining who will carry a concealed weapon in his or her courtroom; any polling place; any meeting of the governing body of a county, public school district, municipality, or special district; any meeting of the Legislature or a committee thereof; any school, college, or professional athletic event not related to firearms; any school administration building; any portion of an establishment licensed to dispense alcoholic beverages for consumption on the premises, which portion of the establishment is primarily devoted to such purpose; any elementary or secondary school facility; any career center; any college or university facility unless the licensee is a registered student, employee, or faculty member of such college or university and the weapon is a stun gun or nonlethal electric weapon or device designed solely for defensive purposes and the weapon does not fire a dart or projectile; inside the passenger terminal and sterile area of any airport, provided that no person shall be prohibited from carrying any legal firearm into the terminal, which firearm is encased for shipment for purposes of checking such firearm as baggage to be lawfully transported on any aircraft; or any place where the carrying of firearms is prohibited by federal law. Any person who willfully violates any provision of this subsection commits a misdemeanor of the second degree, punishable as provided in s. 775.082 or s. 775.083."
Since bank is not mentioned, I believe you would be fine. Especially, since one of the grounds for issuing a permit is for business owners to carry receipts to the bank.
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