Captain reported a bleed air valve malfunction affecting the anti icing systems occurred in cruise flight and resulted in a diversion.

Narrative

Upon departure from ZZZ airport; the non-flying pilot performing the after takeoff flow and checklist. After completed not long after takeoff; the aircraft entered icing conditions. I was still hand flying the aircraft as is normal procedure for that phase of flight. Noticing the 4 valves required to open in icing conditions to ensure that the aircraft was properly receiving bleed air to the appropriate surfaces I returned back to hand flying the airplane. A few seconds after entering icing conditions; we got a master caution warning and a Bleed 1 Leak. The non-flying Pilot was monitoring the bleed leak temperatures and commented that the Bleed Leak notification even before the bleed temperatures heated up. We ran the Bleed Leak Checklist. While running the bleed one leak checklist a bleed 2 overheat occurred and I reduced thrust lever angle and that seemed to resolve the issue. We exited icing conditions and the aircraft returned to normal operation however the bleed 1 leak remained. After running the bleed leak checklist we reduced the #1 engine thrust lever angle; as the checklist instructed and approximately 15 minutes after #1 engine TLA (Thrust Lever Angle) to idle; the Bleed 1 Leak notification went away. After the non-flying Pilot and I conferred about our options; we asked ATC to remain at 25;000 ft. and instructed ATC that we would be diverting from our original destination of ZZZ1 to ZZZ2. We did not [request priority handling] and we continued for approximately 45 minutes to ZZZ2 and landed without further incident at ZZZ2 airport.