B737-800
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Total 23000
Human-Machine Interface; Other / Unknown
ATC Issue All Types; Aircraft Equipment Problem Less Severe; Conflict NMAC; Deviation / Discrepancy - Procedural Published Material / Policy
Flight Crew Took Evasive Action
ATC Equipment / Nav Facility / Buildings; Human Factors; Procedure
40 miles north of RNO at 10;000 feet MSL; in a holding pattern assigned by ATC; as we were accomplishing the checklist for a flap asymmetry malfunction.  A TCAS advisory had traffic at our 12:30 and 12 miles; indicating 1000 ft. above our altitude and heading toward us/converging flight paths. At five miles traffic was now 12:00 and 500 feet above our altitude.  At 3 miles and 12:00 traffic was descending and indicating 300 feet above us. We took evasive action; turning away 90 degrees and descending over 700 feet. Traffic ultimately crossed to our right 500 feet above our altitude while we executed the evasive maneuver. TCAS gave a visual RA after we executed our evasive maneuver; but it gave no aural RA. We notified ATC of our actions and our subsequent return to heading and altitude. ATC stated that according to his radar traffic was 1000 feet above our altitude. I believe oncoming traffic was a general aviation aircraft off his altitude. We never acquired the traffic visually.  We called out traffic early to ATC; but his radar showed a 1000 feet of clearance.  We on the other hand could not risk such a near miss encounter and chose to take aggressive and decisive action to avoid the oncoming traffic; ultimately violating our ATC clearance.  Conditions were VFR and no other traffic was in our area.
B737-800 Captain reported TCAS indicating NMAC which resulted in evasive action although ATC stated traffic indicated 1000 feet vertical separation.