TITLE: Translate this logical statement into natural language.
QUESTION [6 upvotes]: I am trying to translate this logical statement into English: $\forall x(x<10 \implies \forall y(y < x \implies y < 9))$. 
Note that the statement is true when the universe of discourse is $\mathbb{N}$.The best sentence I could come up with was "all numbers less than any number that is less than 10 are also less than 9." Is there a more clear way to translate this statement?
EDIT: The English statement should not include variables or statements such as "for all".

REPLY [2 votes]: tl;dr–  If $y<x<10 ,$ then $y < 9 .$

$$
\underbrace{\forall x}_{\text{For any}~x,}
(
\underbrace{x<10}_{\begin{array}{c}x~\text{being less}\\[-25px]\text{than 10}\end{array}}
\underbrace{\implies}_{\begin{array}{c}\text{implies}\\[-25px] \text{that},\end{array}}
\underbrace{\forall y}_{{\begin{array}{c}\text{for}\\[-25px]\text{any}~y,\end{array}}}
(
\underbrace{y < x}_{{\begin{array}{c}y~\text{being less}\\[-25px]\text{than}~x,\end{array}}}
\underbrace{\implies}_{\begin{array}{c}\text{implies}\\[-25px] \text{that}\end{array}}
\underbrace{y < 9}_{\begin{array}{c}y~\text{is less}\\[-25px]\text{than}~9.\end{array}}
)
)
$$

$$
\underbrace{\forall x}_{\text{For any}~x,}
(
\underbrace{x<10}_{\begin{array}{c}\text{if}~x~\text{is}\\[-25px] \text{less} \\[-25px]\text{than 10}\end{array}}
\underbrace{\implies}_{\text{then}}
\underbrace{\forall y}_{{\begin{array}{c}\text{for}\\[-25px]\text{any}~y,\end{array}}}
(
\underbrace{y < x}_{{\begin{array}{c}\text{if}~y~\text{is}\\[-25px]\text{less}\\[-25px]\text{than}~x,\end{array}}}
\underbrace{\implies}_{\text{then}}
\underbrace{y < 9}_{\begin{array}{c}y~\text{is less}\\[-25px]\text{than}~9.\end{array}}
)
)
$$

$$
\underbrace{x<10}_{\begin{array}{c}\text{If}~x~\text{is}\\[-25px] \text{less} \\[-25px]\text{than 10}\end{array}}
\underbrace{\implies}_{\text{then}}
\underbrace{y < x}_{{\begin{array}{c}\text{if}~y~\text{is}\\[-25px]\text{less}\\[-25px]\text{than}~x,\end{array}}}
\underbrace{\implies}_{\text{then}}
\underbrace{y < 9}_{\begin{array}{c}y~\text{is less}\\[-25px]\text{than}~9.\end{array}}
$$

$$
\underbrace{x<10 \implies y < x}_{\begin{array}{c}\text{If}~x~\text{is less than 10} \\[-25px] \text{and} \\[-25px] \text{if}~y~\text{is less than}~x,\end{array}}
\underbrace{\implies}_{\text{then}}
\underbrace{y < 9}_{\begin{array}{c}y~\text{is less}\\[-25px]\text{than}~9.\end{array}}
$$