my problem is like this: I have a problem, I solve it, I arrive for instance to conclusion like this:

(1) x=y

(2)x+z=f

so once I arrive to the second equation which is x+z=f, in my head I know that's x=y, but what's confusing me is, is it legitimate to go to the first equation and afterwards going to the second equation for assigning ? I mean I know x=y, but who said that's legal to take myself to the first equation, grabbing data from their, and going with those data to the second equation and manipulate the grabbed data over the second equation?

once again, my problem isn't that I don't know that x=y or whatever, again and again, once I reach the second equation x+z=f, totally I know and still remember that x=y, but my confusion is, who said that it's legal to go to the first equation and grabbing from their the logic of the first equation, and manipulate that logic to the second equation?!!! here's totally my point!

Anyone can help me by an analogy to our real life that "manipulating LOGIC of first equation to the other equations is totally legitimate" and going, grabbing from equations and connect between them is "throughout true" and not mess the logic.

to clear more, who said it's legal to "go" from logic of first equation to manipulate it over other equations? is "going" something legal?

Sorry once again for that but I'm struggling that problem