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When applying a rule of inference, is it okay to "skip" a step (i.e, apply a same rule to multiple parts of a statement)?
For example:
(A > B) ^ (C > D)
(~A v B) ^ (~C v D) 1, Impl.
As opposed to applying simplification first, then implication on each statement alone (resulting in more lines).
It seems like more of a stylistic point, but I'm curious and would like to keep to best practices.
In general, I would say YES, unless the problem explicitly asks for a detailed step-by-step proof "mechanically" testable.
But you have to take care of what rules are you using.
Consider the set of rules referred into the post : step-by-step natural deduction.
As you can see, there are two types of rules :
those, called "conditionally true", that cannot be applied to a sub-formula inside a formula;
and :
those that are "biconditional rules" (called : rules of equivalence), that can be applied substituting a sub-formula inside a formula.
