Is there an opposite of proof by contradiction?

Question

Suppose I want to prove $a=b$.

I start by assuming $a=b$. I simplify the expressions and arrive at something which is always true like $1=1$. Does this mean that the original statement is true?

Answer 1

This is called circular reasoning and it's not sound because you're assuming the conclusion to begin with.

Answer 2

Are you referring to Deduction? Typically this is not done, you usually do it in reverse, arriving at the statement you want to prove from something you know to be true like $1=1$ by reasoning deductively and manipulating both sides of the equation.

Answer 3

$-1=1 \implies (-1)^2=1^2 \implies 1=1$.

But $-1=1$ is obviously not true.