let f, g be sequence of SetPrimes; :: thesis: ( ( for n being Nat holds f . n = primenumber n ) & ( for n being Nat holds g . n = primenumber n ) implies f = g )
assume that
A2: for n being Nat holds f . n = primenumber n and
A3: for n being Nat holds g . n = primenumber n ; :: thesis: f = g
let n be Element of NAT ; :: according to FUNCT_2:def 8 :: thesis: f . n = g . n
thus f . n = primenumber n by A2
.= g . n by A3 ; :: thesis: verum