Define free occurrence and bound occurrence of a variable. DO this not using the recursive definition but as follows. If an occurrence of variable x occurs within a quantification that uses a dummy x, then the occurrence is bound to the closest such dummy. If the occurrence does not occur within such a quantification, it's a free occurrence of x. 2. Extend definition of textual substitution to cover quantification, as on page 147.
Textual substitution gives something illegal.
New Leibniz definition to cover quantification . Axioms for all quantifications. This should be enough to cover the lecture, if one provides enough examples. If there is time, 5. Change of dummy.