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