You can set up a regular expression that will match any of the elements of @all then read each line and split, passing the original line and each column out of a map to grep the second columns that match, finally maping out the original line and printing it.

use strict;
use warnings;

my @wanted = qw{7723 7725 9908 7765 7874};
my $rxExtract;
{
    local $" = q{|};
    $rxExtract = qr{\b@wanted\b};
}

print
   map  { $_->[0] }
   grep { $_->[2] =~ $rxExtract }
   map  { [ $_, split ] }
   <DATA>;

__END__
77876    8543    CA84985    54E
77873    8003    CA84985    54E
77875    7725    CA84985    54E
77872    8511    CA84985    54E
77873    8123    CA84985    54E
77822    9908    CA84985    54E
77819    8503    CA84985    54E
77826    8040    CA84985    54E
77822    7874    CA84985    54E
77884    8543    CA84985    54E
77809    7211    CA84985    54E
[download]

The output is

77875    7725    CA84985    54E
77822    9908    CA84985    54E
77822    7874    CA84985    54E
[download]

I hope this is of use.

Cheers,

JohnGG