en_tn_lite_do_not_use/gal/03/21.md

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against the promises

"opposed to the promises" or "in conflict with the promises"

if a law had been given that could give life

This can be stated in active form, and the abstract noun "life" can be translated with the verb "live." Alternate translation: "if God had given a law that enabled those who kept it to live" (See: rc://en/ta/man/translate/figs-activepassive and rc://en/ta/man/translate/figs-abstractnouns)

righteousness would certainly have come by the law

"we could have become righteous by obeying that law"