Sufficient justification for a proposition of the form A such that B implies C By the definition of implies, if the statement C is always true then B implies C is always true.  Is proving C is always true sufficient to show A such that B implies C is always true?
A in the context of the question I am considering is for all epsilon greater than 0 there exists a delta greater than 0 such that...
Clarification 1: Form of Question
Clarification 2: The question is in regards to complex limits.  I've added further clarification: Complex Limits Question
 A: This is a question concerning the difference between 1st order logic and 2nd order logic. In first order logic, we have things like

$A\to B$ (which means $A$ implies $B$ or $B$ is inferred from $A$)

First order logic uses things like "truth tables". In second order logic, we have statements that are true or false within scope (additionally, true or false are now apart of what is called an "interpretation"). Scope is defined by a set. A set is a collection of elements. An element is a member of a set. Both set and element have circular definitions (which is guaranteed to occur somewhere in any finite language of words).
Technically, there is only one "scope" symbol, know as $\forall$; which discusses all elements of a set. The other symbol, $\exists$ is simply short hand for $\sim\forall\sim$. In general, statements now look like

$\forall x\in S, A(x)\to B(x)$ (or for simplicity $\forall S, A\to B$)

The symbols $(x)$ and $x\in$ are unecessary and only serve to provide clarification to the language. They serve no purpose for the logic. In such a second order system the concept of "truth tables" doesn't make sense anymore. Instead what matters is the elements in $S$ and how they are used. Second order logic is much more complicated than first order logic; although there are obvious parallels at times.
Disconnecting $A\to B$ from it's scope, $\forall S$ is just a violation of how the 2nd order logical system is defined. It would make no sense to do so.
I highly recommend a class on "logic for mathematicians/philosophers", it would go over these things in great detail; including Godel's awe-dropping result on incompleteness of arithmetic.
