Validly

val·id  (vld)

adj.

1. Well grounded; just: a valid objection.

2. Producing the desired results; efficacious: valid methods.

3. Having legal force; effective or binding: a valid title.

4. Logic

a. Containing premises from which the conclusion may logically be derived: a valid argument.

b. Correctly inferred or deduced from a premise: a valid conclusion.

5. Archaic Of sound health; robust.

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[French valide, from Old French, from Latin validus, strong, from valre, to be strong; see wal- in Indo-European roots.]

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va·lidi·ty, valid·ness n.

valid·ly adv.

Synonyms: valid, sound², cogent, convincing
These adjectives describe assertions, arguments, conclusions, reasons, or intellectual processes that are persuasive because they are well founded. What is valid is based on or borne out by truth or fact or has legal force: a valid excuse; a valid claim.
What is sound is free from logical flaws or is based on valid reasoning: a sound theory; sound principles.
Something cogent is both sound and compelling: cogent testimony; a cogent explanation.
Convincing implies the power to dispel doubt or overcome resistance or opposition: convincing proof.

Thesaurus

Adv.

1.

validly - with validity; in a valid manner; "this may not validly be done"