Etymology
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valediction (n.)
"a farewell, a bidding farewell," 1610s, from past participle stem of Latin valedicere "bid farewell, take leave," from vale "farewell!," second person singular imperative of valere "be well, be strong" (from PIE root *wal- "to be strong") + dicere "to say" (from PIE root *deik- "to show," also "pronounce solemnly").
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valedictory (adj.)
1650s, "pertaining or relating to leave-taking," from Latin valedictum (past participle of valedicere; see valediction) + -ory. As a noun meaning "valedictory address" from 1779.
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*wal- 

Proto-Indo-European root meaning "to be strong."

It forms all or part of: ambivalence; Arnold; avail; bivalent; convalesce; countervail; Donald; equivalent; evaluation; Gerald; Harold; invalid (adj.1) "not strong, infirm;" invalid (adj.2) "of no legal force;" Isold; multivalent; polyvalent; prevalent; prevail; Reynold; Ronald; valediction; valence; Valerie; valetudinarian; valiance; valiant; valid; valor; value; Vladimir; Walter; wield.

It is the hypothetical source of/evidence for its existence is provided by: Latin valere "be strong, be well, be worth;" Old Church Slavonic vlasti "to rule over;" Lithuanian valdyti "to have power;" Celtic *walos- "ruler," Old Irish flaith "dominion," Welsh gallu "to be able;" Old English wealdan "to rule," Old High German -walt, -wald "power" (in personal names), Old Norse valdr "ruler."

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*deik- 
Proto-Indo-European root meaning "to show," also "pronounce solemnly," "also in derivatives referring to the directing of words or objects" [Watkins].

It forms all or part of: abdicate; abdication; addict; adjudge; apodictic; avenge; benediction; betoken; condition; contradict; contradiction; dedicate; deictic; deixis; dictate; diction; dictionary; dictum; digit; disk; ditto; ditty; edict; Eurydice; index; indicate; indication; indict; indiction; indictive; indite; interdict; judge; judicial; juridical; jurisdiction; malediction; malison; paradigm; policy (n.2) "written insurance agreement;" preach; predicament; predicate; predict; prejudice; revenge; soi-disant; syndic; teach; tetchy; theodicy; toe; token; valediction; vendetta; verdict; veridical; vindicate; vindication; voir dire.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit dic- "point out, show;" Greek deiknynai "to show, to prove," dike "custom, usage;" Latin dicere "speak, tell, say," digitus "finger," Old High German zeigon, German zeigen "to show," Old English teon "to accuse," tæcan "to teach."
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