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Read article 4 of Humane Vitae for the biblical basis for the Catholic Church interpreting the moral law.
Then Evangelium Vitae may begin to make sense.
This moral condemnation also regards procedures that exploit living human embryos and fetuses-sometimes specifically "produced" for this purpose by in vitro fertilization-either to be used as "biological material" or as providers of organs or tissue for transplants in the treatment of certain diseases. The killing of innocent human creatures, even if carried out to help others, constitutes an absolutely unacceptable act.
Given the sanctity of every human person, known before they were formed in their mother's womb, the secondary effects of in vitro fertilization certainly fall under "Thou Shall not Kill".
The rest of course falls under the natural moral law as gmoothart says, which is, you ask "where ought a person be conceived" and the answer is "whereever the egg is hanging out during the marital act".
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The Catholic Church objects to IVF, primarily on grounds that it comes from reasoning from natural law rather than grounded by a teaching from the Bible.
It is common practice in IVF to fertilize several eggs to increase the likelihood that one of them will survive for implantation and then selectively abort or cryogenically freeze the "extra" babies. The Roman Catholic position is that Christians should oppose that practice for the same reasons they oppose abortion.