Linearizing If-Then condition

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Somewhere in the internet, I have read that,

suppose, $x, y \in \mathbb{R}, ~and, ~~~ z \in \lbrace 0,1 \rbrace$

$\text{if}~ x>y, ~\text{then,}~ z = 0 \implies \text{if}~ z = 1, ~ \text{then,}~ x \leq y$

It will be great if anyone has any reference to prove this fact.

P.S. I have lost the slide where I was introduced to this fact. And after a days search, I still did not manage to find that particular reference.

N.B. Please point to to correct forum, if I have asked to the wrong site.