In proof theory, a proof of a formula $\phi$ in which the final step is an application of the corresponding introduction rule for $\phi$, i.e., the introduction rule for the principal connective of $\phi$. For example, a canonical proof of a conjunction $\phi \wedge \psi$ will be a proof of the following form:

The notion of a canonical proof is important to the philosophy of language espoused by philosopher Michael Dummett (1925–2011), in which truth conditions for connectives are eschewed in favour of assertability conditions. Because introduction rules for a connective can be seen as essential to the meaning of that connective by describing the occasions in which formulae with that connective can be asserted, a canonical proof of $\phi$ provides a direct licence of sorts for the assertion of $\phi$.