The last rule of inference is universal generalization (UG). It has the following form:

We can now state the restrictions on universal generalization. Universal generalization is valid, if, but only if:

1. a was introduced by UI or in the assumption of a conditional or reductio proof (not in a premise or by EI).

2. The inference does not occur within a conditional or reductio proof whose assumption contains a.

3. The statement ...a... does not contain any other name introduced by EI on a line containing a.