A CRJ-900 PILOT REPORTED A BLEED AIR LEAK IN THE ANTI-ICE DUCT AFTER DEPARTING IN ICING CONDITIONS DISABLING THE ANTI-ICE SYSTEM. FOLLOWING QRH PROCEDURES THE CREW CONTINUED TO THEIR COLD IMC DESTINATION WITH NO PROBLEM.

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WE DEPARTED FROM ZZZ IN ICING CONDITIONS AND CLIMBED OUT ON THE DEPARTURE. THE WING AND THE COWL ANTI-ICE WERE ON FOR TAKEOFF AND THE DEPARTURE PHASE OF FLIGHT. AT APPROX FL210 IN THE CLIMB WE RECEIVED A TRIPLE CHIME MASTER WARNING ASSOCIATED WITH THE ANTI-ICE DUCT WARNING MESSAGE. WITHIN 1 MINUTE; THE MESSAGE BECAME AN ANTI-ICE DUCT CAUTION MESSAGE ASSOCIATED WITH AN ICE CAUTION MESSAGE. WE FOLLOWED THE QRH PROCEDURE WHICH INDICATED THAT WE WERE NO LONGER TO FLY IN ICING CONDITIONS. DUE TO WEATHER CONDITIONS ALONG OUR ROUTE OF FLIGHT; TOWARDS THE ALTERNATE AND ANYWHERE WE HAD FUEL TO GO; THIS WAS IMPOSSIBLE. WE CLIMBED TO GET OUT OF THE CURRENT ICING AND AT SOME POINT IN TIME WE WOULD HAVE TO DESCEND BACK THROUGH A CLOUD LAYER. WE CONTACTED DISPATCH AND DECIDED THAT DUE TO CURRENT CONDITIONS AND PIREPS; ZZZ1 WAS STILL OUR BEST OPTION FOR LEAST ICING CONDITIONS. OUR BACKUP WAS ZZZ2. FOLLOWING COMPANY PROCEDURES; I LEFT THE FLIGHT DECK TO VISUALLY ENSURE THAT THERE WAS NO ICE BUILDUP ON THE LEADING EDGE OF THE WING AND FOUND BOTH WINGS TO BE CLEAR OF ICE. WE NOTIFIED THE FLIGHT ATTENDANTS OF THE SITUATION AND LABELED IT AN EMERGENCY; AS WE WERE GOING TO HAVE TO DECLARE AN EMERGENCY WHEN WE WOULD BE FLYING IN ICING CONDITIONS WITH NO WING ANTI-ICE. CAPTAIN THEN CAME UP WITH THE IDEA TO ENLIST THE HELP OF A DEADHEADING PILOT; AND WE HAD THE FLIGHT ATTENDANT POSITION HIM IN A ROW SO AS TO SEE THE LEADING EDGE OF THE AIRCRAFT WING AND NOTIFY US IMMEDIATELY OF ANY ICE BUILDUP. WE CHECKED BACK IN WITH DISPATCH; AND TAKING INTO ACCOUNT THE PIREPS AND THE WEATHER IN ZZZ1; IT WAS STILL OUR BEST OPTION. WE NOTIFIED ATC AND DECLARED AN EMERGENCY DUE TO NO ANTI-ICE HEADED INTO ANTI-ICE CONDITIONS. IF ICE DID BUILD UP ON THE WINGS DURING APPROACH; THE QRH CALLED FOR US TO LAND AT MUCH HIGHER THAN NORMAL SPEED; SO WE HAD EMERGENCY TRUCKS STANDING BY. WE STAYED HIGH AT FL310 AND THEN CAME DOWN AT AROUND 4000 FPM. WE ALSO NOTIFIED ATC THAT WE WOULD BE MAINTAINING 300 KTS BELOW 10000 FT SO AS TO MAINTAIN THE HIGHEST TAT AS POSSIBLE AND AVOID ICING. WE LEVELED AT 4000 FT BELOW THE LOWEST CLOUD DECK AND SUCCESSFULLY AVOIDED ACCRUING ANY ICE ON THE AIRCRAFT. CAPTAIN LANDED THE AIRCRAFT ON RUNWAY 12R SUCCESSFULLY AND WE EXITED THE RUNWAY AND CANCELED THE EMERGENCY. THE EVENT OCCURRED DUE TO A MECHANICAL MALFUNCTION OF THE AIRCRAFT AND A BLEED AIR LEAK IN THE ANTI-ICE DUCT.