# Introduction to Proofs

Reference > MathematicsAn explanation of proofs, along with some simple examples

Examples of more algebraic proofs which use additional properties, like the Substitution Property

Using definitions of mathematical terminology in proofs

An explanation of theorems, and how we can use them in proofs

How to use the transitive property in proofs

How to prove something by using an assumption that leads to a contradiction

In which we create another algebraic theorem, using two lemmas to help us out

An explanation of corollaries, with some non-geometric examples

Moving beyond two-column proofs to more fluid paragraph style proofs

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