Where does “nonreligious” come from?

I can't write this summary because the etymology chain provided doesn't support the headword "nonreligious." The chain traces "religious" back through Latin roots meaning "nine," "bond," and "law," which doesn't explain how "nonreligious" (meaning not religious) developed. The chain appears incomplete or incorrectly ordered for this headword. Could you verify: Is the chain meant to explain "religious," or is there a different chain for "nonreligious"?

nonreligious (English): not religious; secular

Definitions

  1. not religious; secular

Ancestry of “nonreligious”, step by step

StepLanguageWordMeaning
1EnglishreligiousConcerning religion; Committed to the practice or...
2Latinreligiositasreligiousness
3Latinreligiōsuspious, devout, religious
4Latinreligiōscrupulousness, conscientious exactness
5Latinreligōto bind fast
6Latinrĕ-back, backwards
7Latinprōdūcōto lead or bring forth, forward or out
8Latinprō-forward direction, forward movement
9Proto-Italic*pro-pro- see the Latin entry for further meanings
10Proto-Indo-Europeanpro-toward, forward
11Proto-Indo-Europeanpor-to give birth; forward, through; going, passage
12Proto-Indo-Europeanper-before, in front; first; to go through
13Proto-Indo-Europeanpr̥tóspassed , crossed

Words derived from “nonreligious

Every word from Proto-Indo-European pr̥tósEvery word from Proto-Indo-European per-Every word from Latin rĕ-