cant validate and insert date on form - php

Question

im trying to create a form that validates the input fields then sends the data into a mysql database. i can get either the input validation to work, or the data inserted into the database, but not both.. heres my code:
<?php require_once('../php/pdo_connect.php');
// define variables and set to empty values
$first_name_err = $last_name_err = $cell_err = $email_err = FALSE;
$first_name = $last_name = $cell = $email = FALSE;
if ($_SERVER["REQUEST_METHOD"] == "POST")
{
if (empty($_POST["first_name"]))
{$first_name_err = "First name is required";}
else
{
$first_name = test_input($_POST["first_name"]);
// check if name only contains letters and whitespace
if (!preg_match("/^[a-zA-Z ]*$/",$first_name))
{
$first_name_err = "Please don't use hypens or other special characters";
}
}
if (empty($_POST["last_name"]))
{$last_name_err = "Last name is required";}
else
{
$last_name = test_input($_POST["last_name"]);
// check if name only contains letters and whitespace
if (!preg_match("/^[a-zA-Z ]*$/",$last_name))
{
$last_name_err = "Please don't use hypens or other special characters";
}
}
if (empty($_POST["cell"]))
{$cell_err = "Phone number is required";}
else
{
$cell = test_input($_POST["cell"]);
// check if name only contains letters and whitespace
if (!preg_match("/^[\+0-9\-\(\)\s]*$/",$cell))
{
$cell_err = "Invalid cell phone number";
}
}
if (empty($_POST["email"]))
{$email_err = "Email address is required";}
else
{
$email = test_input($_POST["email"]);
// check if e-mail address syntax is valid
if (!preg_match("/([\w\-]+\#[\w\-]+\.[\w\-]+)/",$email))
{
$email_err = "Invalid email format";
}
}
if ($first_name_err = false){
//insert info into db
$query = $pdo->prepare("INSERT INTO `guestlist_page_requests` (first_name, last_name, cell, email) VALUES (?, ?, ? ,?)");
$query->bindValue(1, $first_name);
$query->bindValue(2, $last_name);
$query->bindValue(3, $cell);
$query->bindValue(4, $email);
$query->execute();
header('Location: ../index.php');
}else{
//not enough data to submit to db
}
}
i tried a few differant variations of this line:
if ($first_name_err = false){
but im not really sure what i should be putting here?
this line almost makes it work:
if (!empty($_POST['first_name']) && !empty($_POST['last_name']) && !empty($_POST['cell']) && !empty($_POST['email'])){
but then it submits the data with the errors unless one of the fields is empty.
this also doesnt seem to work right:
if ($first_name_err = false){