Ordering of two real numbers

Question

Is the below true for $a\in\mathbb{R},\,b\in\mathbb{R}$? $$ (a \geq b) \iff (\forall \gamma\in\mathbb{R}: b\geq\gamma\implies a\geq\gamma) $$ The $\implies$ direction is obvious; the $\impliedby$ direction feels weird because of the "$\forall$" quantifier. Is "$\forall$" necessary, or can it be replaced with something weaker?