Catalyzes the reversible conversion of 5-aminoimidazole ribonucleotide (AIR) and CO(2) to 4-carboxy-5-aminoimidazole ribonucleotide (CAIR). Does not accept N5-carboxyaminoimidazole ribonucleotide (N5-CAIR) as a substrate. 5-amino-1-(5-phospho-D-ribosyl)imidazole-4-carboxylate + H(+) = 5-amino-1-(5-phospho-beta-D-ribosyl)imidazole + CO2 kcat is 77 sec(-1). Purine metabolism; IMP biosynthesis via de novo pathway; 5-amino-1-(5-phospho-D-ribosyl)imidazole-4-carboxylate from 5-amino-1-(5-phospho-D-ribosyl)imidazole (carboxylase route): step 1/1. Belongs to the AIR carboxylase family. Class II subfamily.