In a formal system of reasoning, such as mathematics, a statement is necessarily true if it is true for all the values that can be assigned to its variables. Generally speaking, this means that the truth of the statement can be determined by symbolic manipulation as opposed to the assigning values and testing the results.
A symbolic constant in such an expression may be thought of as a variable that we hold at a constant value while we allow other variables to change. In mathematics, for example, this simplifies certain operations, such as the differentiation of algebraic functions, but that’s not the key point here.
The expression, “Consider a>b, if b>c, then a>c is necessarily satisfied.” is simple, logical and correct. From it, the reader can infer that it is only necessary to compare a against the larger of the two constants b and c.
The expression is given in isolation, so we don’t know the form of the argument that follows. However, consider is typically used in this context to establish a point in the reader’s mind, so that it can be referred to further along.
Most of the suggestions advanced by the commenters are technically correct, but are needlessly heavy and burdensome to the text.
Style, of course, is a matter of opinion, and de gustibus non est disputandum, but in my opinion the original was fine.
The ever-useful Wikipedia has quite a lot to say about logic: https://en.m.wikipedia.org/wiki/Logic
