let C, D, C9 be Category; :: thesis: for S being Functor of [:C,C9:],D
for c being Object of C
for c9 being Object of C9 holds (Obj (S ?- c)) . c9 = (Obj S) . (c,c9)
let S be Functor of [:C,C9:],D; :: thesis: for c being Object of C
for c9 being Object of C9 holds (Obj (S ?- c)) . c9 = (Obj S) . (c,c9)
let c be Object of C; :: thesis: for c9 being Object of C9 holds (Obj (S ?- c)) . c9 = (Obj S) . (c,c9)
let c9 be Object of C9; :: thesis: (Obj (S ?- c)) . c9 = (Obj S) . (c,c9)
(S ?- c) . (id c9) = S . ((id c),(id c9)) by FUNCT_5:69
.= S . (id [c,c9]) by Th25
.= id ((Obj S) . [c,c9]) by CAT_1:68 ;
hence (Obj (S ?- c)) . c9 = (Obj S) . (c,c9) by CAT_1:67; :: thesis: verum