Dictionary:

a fortiori

  (ä fôr'tē-ôrrī')

For a still stronger reason; all the more.

[Latin : ā, ab, from + fortiōrī, ablative of fortior, stronger.]

ADVERTISEMENT

(Latin, from the stronger) Phrase used for ‘all the more’ or ‘even more so’: if all donkeys bray, then a fortiori all young donkeys bray.

[Latin, With stronger reason.] This phrase is used in logic to denote an argument to the effect that because one ascertained fact exists, therefore another which is included in it or analogous to it and is less improbable, unusual, or surprising must also exist.

All the more so, with greater reason

The adverb has one meaning:

Meaning #1: for a still stronger, more certain reason
  Synonyms: with greater reason, with more reason