let D, D9, E be non empty set ; for d being Element of D
for d9 being Element of D9
for i being natural Number
for F being Function of [:D,D9:],E holds F [;] (d,(i |-> d9)) = i |-> (F . (d,d9))
let d be Element of D; for d9 being Element of D9
for i being natural Number
for F being Function of [:D,D9:],E holds F [;] (d,(i |-> d9)) = i |-> (F . (d,d9))
let d9 be Element of D9; for i being natural Number
for F being Function of [:D,D9:],E holds F [;] (d,(i |-> d9)) = i |-> (F . (d,d9))
let i be natural Number ; for F being Function of [:D,D9:],E holds F [;] (d,(i |-> d9)) = i |-> (F . (d,d9))
let F be Function of [:D,D9:],E; F [;] (d,(i |-> d9)) = i |-> (F . (d,d9))
thus F [;] (d,(i |-> d9)) =
F .: ((i |-> d),(i |-> d9))
.=
i |-> (F . (d,d9))
by Th17
; verum