Catalyzes the conversion of urocanate to 4-imidazolone-5-propionate. 4-imidazolone-5-propanoate = H2O + trans-urocanate Binds 1 NAD(+) per subunit. Amino-acid degradation; L-histidine degradation into L-glutamate; N-formimidoyl-L-glutamate from L-histidine: step 2/3. Belongs to the urocanase family.