Linear programming problem minimization change problem

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minimize $max ${x1,x2}

subject to
$2x1+5x2<=9$
$x1+3x2<=5$
$x1>=0$, $x2>=0$

show that both are same and give reason

minimize t
subject to t>=x1 , t>=x2
$2x1+5x2<=9$
$x1+3x2<=5$
x1>=0, x2>=0

i tried
let t>=max{x1,x2}
then t>=x1 and t>=x2
am i right? but i dont understand the reason. please give me some hint thankyou