Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Situational Awareness
ATC Issue All Types; Conflict NMAC
Air Traffic Control Issued Advisory / Alert; Flight Crew FLC complied w / Automation / Advisory
Procedure; Human Factors
While we departed Ontario; CA on the RAJEE3 departure; ATC asked us to maintain 7;000 feet. Close to the RAJEE checkpoint ATC called two targets:1) [A] Small Aircraft; 12 o' clock; 7 miles; 6;500 feet. 2) A Medium Large Transport 8;000 [feet] at 10 o' clock.We responded searching for the Small Aircraft and called the Medium Large Transport in sight. ATC again called our attention to the Small Aircraft 12 o' clock five miles to which we responded searching. Many other calls not related to us continued over the frequency when we received an RA from the TCAS indicating adjust vertical speed. Looking at the VSI the vertical speed showed to remain level. We spot the Small Aircraft on TCAS converging but only visually picked out the aircraft less than 1/4 mile (hazy outside) at 10 o' clock (not 12 o' clock) passing directly underneath us 300 feet. TCAS indicated clear of conflict as the Small Aircraft passed to our five o'clock. The next call from ATC was traffic passing behind us and climb to 13;000 feet. Meanwhile; the Medium Large Transport passes over us.We indicated to ATC that we received a TCAS RA and that the Small Aircraft passed 300 feet below us. ATC departure acknowledged and passed us to center. ATC could have vectored us off the SID to avoid the conflicting traffic.
Air carrier flight crew reported NMAC with another aircraft during climbout from ONT airport.