Axiom:Axiom of Dependent Choice

Also known as
Some sources call this the Axiom of Dependent Choices, reflecting the infinitely many choices made.

This axiom can be abbreviated ADC or simply DC.

Also see
This axiom is a weaker form of the axiom of choice, as shown in Axiom of Choice Implies Axiom of Dependent Choice.

This axiom is also a stronger form of the axiom of countable choice, as shown in Axiom of Dependent Choice Implies Axiom of Countable Choice.