Operations of Inference
In the chapter on Equivalence Transformations, we met the operation of uniform substitution of wffs for propositional variables. This operation preserves validity in the sense that if the substitutions are made in a valid wff, the resulting wff is also valid. That this is so follows from the fact that a wff is valid if it has the value 1 for all possible assignments of truth-values to the variables, provided that each assignment is uniform in the sense that the same value is given to each occurrence of a given variable in the wff. Now every wff has the value 1 or the value 0 for each assignment of truth-values to its variables; and so provided that substitution of wffs for propositional variables is uniform, validity is preserved.