let f, g be UnOp of NAT; :: thesis: ( ( for n being Nat holds f . n = Ackermann (m,n) ) & ( for n being Nat holds g . n = Ackermann (m,n) ) implies f = g )
assume that
A2: for n being Nat holds f . n = H₁(m,n) and
A3: for n being Nat holds g . n = H₁(m,n) ; :: thesis: f = g
let n be Element of NAT ; :: according to FUNCT_2:def 8 :: thesis: f . n = g . n
thus f . n = H₁(m,n) by A2
.= g . n by A3 ; :: thesis: verum