LTT FLC DEPARTS VFR FOR IFR FLT PLAN ACTIVATION IN THE AIR. PRIOR TO CONTACT WITH APCH THEY ENTER 2 RESTR AREAS.

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WE WERE VFR ON TKOF OUT OF NOGALES; AZ; BUT HAD FILED AN IFR FLT PLAN. I GAVE MY STANDARD TKOF BRIEFING AND INFORMED MY FO THAT WE WOULD PICK UP OUR IFR CLRNC AS SOON AS WE COULD AFTER TKOF. I WAS CONCERNED ABOUT ENTERING TUCSON'S AIRSPACE AND DECIDED TO STAY TO THE E OF TUCSON ON CLBOUT. OUR PRIMARY NAVAID WAS OUR GPS AND WE WERE HEADING DIRECT TO DENVER; CO. WE MADE OUR LAST CALL TO NOGALES TFC AND STARTED OUR CLB TO 17500 FT. ON CLBOUT WE MADE SEVERAL ATTEMPTS TO CONTACT BOTH ZAB AND TUCSON APCH. WE FINALLY GOT IN TOUCH WITH TUCSON APCH AND THEY CLRED US TO DENVER. IT TOOK SEVERAL MINS FOR THEM TO GET OUR SQUAWK CODE. WHEN THEY FINALLY DID THEY INFORMED US THAT WE HAD FLOWN THROUGH RESTR AREA 2308A AND 2308B. WE WERE THEN HANDED OFF TO ZAB AND THEY INFORMED US OF THE SAME THING. THE CTR CTLR SAID THAT THE CTLING AGENCY FOR THAT RESTR AREA WAS MAD; BUT THAT SHE MAY BE ABLE TO SMOOTH THINGS OUT. SHE CAME BACK AND TOLD US THAT EVERYTHING WAS FINE. I THANKED HER AND ASKED HER IF I NEEDED TO DO ANYTHING AND SHE SAID BE CAREFUL. I CALLED ZAB FROM DENVER AND SPOKE WITH SEVERAL PEOPLE; INCLUDING 2 SUPVRS. THEY MADE 7 PHONE CALLS AND TOLD ME EVERYTHING WAS ALL RIGHT; THAT I HAD NEVER LOST SEPARATION. THE RADAR CTLR OF THE RESTR AREA KEPT US SEPARATED WHILE WE WERE INSIDE OF THEIR AIRSPACE. I NEGLECTED TO LOOK AT THE LOW ENRTE CHART; APCH PLATE OR THE HIGH ENRTE CHART. THE GPS HAD ALL OF THE SPECIAL USE AIRSPACE AND RESTR AREA WARNINGS TURNED OFF AND THAT WAS OUR PRIMARY MEANS OF NAV. NEXT TIME I TKOF VFR; I WILL LOOK AT ALL OF THE SURROUNDING AIRSPACE TO AVOID FUTURE SITS LIKE THIS ONE.