In order to use deductive reasoning to construct a proof we rely on statements that are accepted to be true.

Deductive reasoning is a fundamental aspect of logical reasoning, particularly in mathematics and formal proofs. It involves using accepted statements, known as axioms or premises, to arrive at a conclusion that must be true if the premises are true. Here are key points regarding the process:

1. Accepted Statements: These are axioms, definitions, and previously proven theorems. They serve as the foundation for further reasoning and argumentation.

2. Logical Steps: Deductive reasoning involves a series of logical steps that link premises to a conclusion. Each step must follow from the previous ones in a valid way.

3. Proof Structure: A typical proof using deductive reasoning starts with known statements, applies logical rules, and derives new statements until reaching the desired conclusion.

4. Validity of the Argument: The conclusion reached through deductive reasoning is only as strong as the premises. If the premises are true and the reasoning valid, the conclusion must also be true.

In summary, deductive reasoning is a systematic method of reasoning that hinges on the truth of accepted statements, leading to conclusions that are logically sound. It is widely used in mathematics to establish the truth of propositions and theorems.