The Talmud's central discussion of Pikuach Nefesh: the obligation to violate Shabbat and virtually all other prohibitions to save a life. R. Yehuda in the name of Shmuel derives this from 'v'chai bahem' — 'you shall live by them,' not die by them. This is the classical source for life overriding prohibition.
וּכְבָר הָיָה רַבִּי יִשְׁמָעֵאל וְרַבִּי עֲקִיבָא וְרַבִּי אֶלְעָזָר בֶּן עֲזַרְיָה מְהַלְּכִין בַּדֶּרֶךְ, וְלֵוִי הַסַּדָּר וְרַבִּי יִשְׁמָעֵאל בְּנוֹ שֶׁל רַבִּי אֶלְעָזָר בֶּן עֲזַרְיָה מְהַלְּכִין אַחֲרֵיהֶן. נִשְׁאֲלָה שְׁאֵלָה זוֹ בִּפְנֵיהֶם: מִנַּיִין לְפִקּוּחַ נֶפֶשׁ שֶׁדּוֹחֶה אֶת הַשַּׁבָּת? נַעֲנָה רַבִּי יִשְׁמָעֵאל וְאָמַר: ״אִם בַּמַּחְתֶּרֶת יִמָּצֵא הַגַּנָּב״ — וּמָה זֶה, שֶׁסָּפֵק עַל מָמוֹן בָּא סָפֵק עַל נְפָשׁוֹת בָּא, וּשְׁפִיכוּת דָּמִים מְטַמֵּא אֶת הָאָרֶץ, וְגוֹרֵם לַשְּׁכִינָה שֶׁתִּסְתַּלֵּק מִיִּשְׂרָאֵל, נִיתָּן לְהַצִּילוֹ בְּנַפְשׁוֹ — קַל וָחוֹמֶר לְפִקּוּחַ נֶפֶשׁ שֶׁדּוֹחֶה אֶת הַשַּׁבָּת.
§ The Gemara relates: It once happened that Rabbi Yishmael, and Rabbi Akiva, and Rabbi Elazar ben Azarya were walking on the road, and Levi HaSadar and Rabbi Yishmael, son of Rabbi Elazar ben Azarya, were walking respectfully behind them, since they were younger and did not walk alongside their teachers. This question was asked before them: From where is it derived that saving a life overrides Shabbat? Rabbi Yishmael answered and said that it is stated: “If a thief be found breaking in and be struck so that he dies, there shall be no blood-guiltiness for him” (Exodus 22:1). Now, if this is true for the thief, where there is uncertainty whether he comes to take money or to take lives, and it is known that bloodshed renders the land impure, since it is stated about a murderer: “And you shall not defile the land” (Numbers 35:34), and it causes the Divine Presence to depart from the Jewish people, as the verse continues: “In the midst of which I dwell, for I the Lord dwell in the midst of the children of Israel” (Numbers 35:34), and even so the home owner is permitted to save himself at the cost of the thief’s life, then a fortiori saving a life overrides Shabbat.