First, the form:
<!DOCTYPE html>
<html>
<head>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
</head>
<body>
<form method="post" action="index.php" id="addForm" name="addForm" enctype="multipart/form-data">
<!--
<input type="submit" class="btns" value="Add" id="submitAdd" name="submitAdd">
</form>
<script>
$('#addForm').submit(function (){
valid = false;
if(valid) {
return true;
} else {
return false;
}
});
</script>
</body>
</html>
Next, the PHP side, it should be [] not (), i.e.
$_POST["submitAdd"]