I need to either prove or disprove this statement.
$(\exists y\in R)(\forall x \in R)(2x-y=3)$
I want to provide a proof by contradiction, so I'm proving the negation
$(\forall y\in R)(\exists x \in R)(2x-y \neq 3)$
Suppose y = 1 and x =3 then $2(3)-3 =5 \neq 3$
therefore $(\exists y\in R)(\forall x \in R)(2x-y=3)$ is false.
From what I'm reading this is sufficient proof, but I can't convince myself this is totally correct, but know of no other way to go about it. Any help would be great. Thanks!