Logically it is a singe proof, but technically it consists of quite a few theorems and lemmas, so this is not a valid comparison. Also proofs in Coq are typically structured and pretty high-level because of all the automation, while metamath proofs look like core dumps :)
${
$d A a b v w x y $. $d B a b v w x y $. $d F a b v w x y $.
$( The ` 2nd ` (second member of an ordered pair) function restricted to a
one-to-one function ` F ` is a one-to-one function of ` F ` onto the
range of ` F ` . (Contributed by Alexander van der Vekens,
4-Feb-2018.) $)
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$}
...