A New Equals Sign - Dot Equals

I think that mathematics could use a new commonly used character to describe certain types of equalities. Typically, the equals sign, = , is used to denote the equality of two quantities. A simple example of this would be



A lot of times, algebraic manipulations of expressions are made and the equals sign is also used. An example of this would be:



In this latter example, I think a unique equality character should be used to distinguish equalities made solely from mathematical manipulation.

So I propose the following a dot equals to denote equalities made solely from mathematical manipulation or evaluation. A simple example being:



Or




Although this symbol is available in unicode and Latex, if the character does not exist an equal with a period ( .= ) could be used. I must note that I have seen this to denote "in the limit of". I do not think this is a common use, and as an alternative a dot underneath the equals sign could be used or anything else similar to an equals sign. This symbol and many others exist in Unicode or Latex. For inspiration, check out all of the unicode symbols here.