$re = '/(?:is|are) ([a-zA-Z0-9- ]+?) if\b/m';
$str = 'A relation is well-defined if each element in the domain is assigned to a unique element in the range.
invertible if and only
A mapping is invertible on sth if and only if it is both one-to-one and onto
infinite set, we give a specific proof for the smallest integer being considered, followed by a generic argument showing that
mathematical induction. Instead of attempting to verify a statement about some subset S of the positive integers N on a case-by-case basis, an impossible task if S is an infinite set, we give a specific proof for the smallest integer being considered, followed by a generic argument showing that if the statement holds for a given case, then it must also hold for the next case in the sequence.';
preg_match_all($re, $str, $matches, PREG_SET_ORDER, 0);
// Print the entire match result
var_dump($matches);
Please keep in mind that these code samples are automatically generated and are not guaranteed to work. If you find any syntax errors, feel free to submit a bug report. For a full regex reference for PHP, please visit: http://php.net/manual/en/ref.pcre.php