The definition of infidel has been bastardized over the years, so your definition is not sufficient.
infidel
An unbeliever with respect to a particular religion, especially Christianity or Islam.
One who has no religious beliefs.
One who doubts or rejects a particular doctrine, system, or principle.
\In"fi*del\, n. One who does not believe in the prevailing religious faith; especially, one who does not believe in the divine origin and authority of Christianity; a Mohammedan; a heathen; a freethinker.
Note: Infidel is used by English writers to translate the equivalent word used Mohammedans in speaking of Christians and other disbelievers in Mohammedanism.
Usage: An infidel, in common usage, is one who denies Christianity and the truth of the Scriptures. Some have endeavored to widen the sense of infidel so as to embrace atheism and every form of unbelief; but this use does not generally prevail. A freethinker is now only another name for an infidel. An unbeliever is not necessarily a disbeliever or infidel, because he may still be inquiring after evidence to satisfy his mind; the word, however, is more commonly used in the extreme sense. A deist believes in one God and a divine providence, but rejects revelation. An atheist denies the being of God. A sceptic is one whose faith in the credibility of evidence is weakened or destroyed, so that religion, to the same extent, has no practical hold on his mind. An agnostic remains in a state of suspended judgment, neither affirming nor denying the existence of a personal Deity.
\In"fi*del\, a. [L. infidelis; pref. in- not + fidelis faithful, fr. fides faith: cf. F. infid[`e]le. See Fidelity.] Not holding the faith; -- applied esp. to one who does not believe in the inspiration of the Scriptures, and the supernatural origin of Christianity
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