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We show that induction over $\Delta(\mathbb R)$-definable well-foundedclasses is equivalent to the reflection principle which asserts that any trueformula of first order set theory with real parameters holds in some transitiveset. The equivalence is proved in primitive recursive set theory (which isweaker than Kripke-Platek set theory) extended by the axiom of dependentchoice.

Set-theoretic reflection is equivalent to induction over well-founded classes