This is also called “Substitution Property of Equality”.
If x=y, then x may be replaced by y in any equation or expression.
Using the above definition:
x=y <– –> “x is replaced by y”
You can probably find several textbooks that tell you either variable (x or y) can be replaced by the other. This is ONLY true if you have both 1) Substitution Property and 2) Symmetry of Equality.
Why are we so stubborn and strict? Because you’ll see this strictness when you go through the work of Peano. He starts with nothing and then starts building math, one rule at a time.
Also, when you are learning to program computers you will have all kinds of fun debugging your programs because of typos and a lack of adherence to the strict nature of the programming language. We believe that your having practice with strict thinking will help you adapt more quickly.
Rob Sterling 