Template:ADC

Template
Include this template at (or near) the bottom of any page which depends, either directly or indirectly, on the Axiom of Dependent Choice.

Usage
This template can be invoked as:

or:

where  is the  page name of a proof which itself depends on the ADC.

If you want this to apply to just one of the proofs of a given theorem, then there exists an optional second parameter which is a number (usually 3 or 4) determining the level of heading that the text of this template appears at. The default is 2 (standard heading) when the template itself is used so as to apply to the entire page.

Note: The current implementation is that only level $4$ is available in this context.

Inclusion of this template will result in the page being added to the Examples of Use of Axiom of Dependent Choice category, and the following being added to the page:

Axiom of Dependent Choice
This theorem depends on the Axiom of Dependent Choice, by way of (link to proof name).

Although not as strong as the Axiom of Choice, the Axiom of Dependent Choice is similarly independent of the Zermelo-Fraenkel axioms.

The consensus in conventional mathematics is that it is true and that it should be accepted.

This depends on the Axiom of Dependent Choice.

Although not as strong as the Axiom of Choice, the Axiom of Dependent Choice is similarly independent of the Zermelo-Fraenkel axioms.

The consensus in conventional mathematics is that it is true and that it should be accepted.