pikuach nefesh – saving a life
The Lord then answered him, and said, Thou hypocrite, doth not each one of you on the sabbath loose his ox or his ass from the stall, and lead him away to watering? And ought not this woman, being a daughter of Abraham, whom Satan hath bound, lo, these eighteen years, be loosed from this bond on the sabbath day?Luke 13:15-16
and answered them, saying, Which of you shall have an ass or an ox fallen into a pit, and will not straightway pull him out on the sabbath day?Luke 14:5
Ye shall therefore keep my statutes, and my judgments: which if a man do, he shall live in them: I am the LORD.Lev 18:5
And I gave them my statutes, and shewed them my judgments, which if a man do, he shall even live in themEzek 20:11
“he shall live in them” implies that the law is followed for life, and not death. That following the law should not be at expense of life (result in death). Note that the life being saved is specific and identifiable (not general or conceptual) and must be done straightway (cannot wait for next day).
A righteous man regardeth the life of his beast: but the tender mercies of the wicked are cruelProv 12:10
Taking care of your livestock is the action of a righteous man, how much more so is the taking care of your family and neighbor.