Remark 50.21.2. The analogues of Weil Cohomology Theories, Lemmas 45.12.2 (splitting principle) and 45.12.3 (chern classes of tensor products) hold for de Rham Chern classes on quasi-compact and quasi-separated schemes. This is clear as we've shown in the proof of Lemma 50.21.1 that all the axioms of Weil Cohomology Theories, Section 45.12 are satisfied.
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