This should get the desired result:
//Initial Array
$events = array
(
array
(
'week-day' => 'tuesday',
'day-date' => 1511841600,
'events_ids' => array( 83417 )
),
array
(
'week-day' => 'wednesday',
'day-date' => 1511913600,
'events_ids' => array( 83419, 12345 )
),
array
(
'week-day' => 'tuesday',
'day-date' => 1511830800,
'events_ids' => array( 83411 )
)
);
//Array to fill
$tuesday_event_ids = array();
foreach($events as $event ):
//if day is tuesday & we have event IDs
if($event['week-day'] === 'tuesday' && count($event['events_ids'])):
foreach($event['events_ids'] as $id):
//Push to array if not already in it
if(!in_array($id,$tuesday_event_ids))
array_push($tuesday_event_ids, $id);
endforeach;
endif;
endforeach;
//should be: array(83417,83411)
var_dump($tuesday_event_ids);
side note: you may want to consider changing the array keys to either be all -
based or all _
based for sanity.