Modus ponens, P è vero quindi Q è vero

Simple rule of inference that states:

$P$ implies $Q$. $P$ is true, therefore $Q$ must also be true

In symbolic statement:

$$P\to Q,P⊢Q$$

See also

• Hilbert’s program was to formalize all of math, disproven by Gödel — Hilbert’s program aimed to reduce all of mathematics to mechanical inference rules like this one
• Gödel’s incompleteness theorems — Gödel showed that even a system grounded in rules like modus ponens cannot prove all truths about itself