I'm going to ask a seemingly silly question.
A simple example: Suppose we know that when $(x,y) \in A$, which is a subset of $R^{2}$, then $x+y=c$, where c is a constant. We also know that $(3,4) \in A$, and we want to find the value of c.
Without much thinking, we would just replace $x$ with 3 and $y$ with 4 in the equation and solve for the constant c.
My question is that why we do this? Why replacing $x$ with 3 and $y$ with 4 would cause the equation to hold?
I know this is about predicate logic and when some values satisfy the premise they would also satisfy the followed statement. But why 'satisfying a statement' equals to 'replacing variables with values and the statement becomes true'?
This has been a simple logic for me all along but I recently find it bothering.