Etymology
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mutually (adv.)

"reciprocally, in a manner of giving and receiving," 1530s, from mutual + -ly (2). The meaning "conjointly, in common" (1590s) is "Held to be an erroneous use" [Century Dictionary]. Mutually exclusive is recorded by 1650s. For mutually assured destruction, see mutual.

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Definitions of mutually

mutually (adv.)
in a mutual or shared manner;
the agreement was mutually satisfactory
Synonyms: reciprocally
From wordnet.princeton.edu