let D, D9, E be non empty set ; :: thesis: for d being Element of D
for d9 being Element of D9
for i being Nat
for F being Function of [:D,D9:],E holds F .: (i |-> d),(i |-> d9) = i |-> (F . d,d9)
let d be Element of D; :: thesis: for d9 being Element of D9
for i being Nat
for F being Function of [:D,D9:],E holds F .: (i |-> d),(i |-> d9) = i |-> (F . d,d9)
let d9 be Element of D9; :: thesis: for i being Nat
for F being Function of [:D,D9:],E holds F .: (i |-> d),(i |-> d9) = i |-> (F . d,d9)
let i be Nat; :: thesis: for F being Function of [:D,D9:],E holds F .: (i |-> d),(i |-> d9) = i |-> (F . d,d9)
let F be Function of [:D,D9:],E; :: thesis: F .: (i |-> d),(i |-> d9) = i |-> (F . d,d9)
[d,d9] in [:D,D9:] by ZFMISC_1:def 2;
then [d,d9] in dom F by FUNCT_2:def 1;
hence F .: (i |-> d),(i |-> d9) = i |-> (F . d,d9) by Th8; :: thesis: verum