let f1, f2 be Function of F₁(),BOOLEAN; :: thesis: ( ( for x being Element of F₁() holds f1 . x = F₂(x) ) & ( for x being Element of F₁() holds f2 . x = F₂(x) ) implies f1 = f2 )
assume that
A1: for x being Element of F₁() holds f1 . x = F₂(x) and
A2: for x being Element of F₁() holds f2 . x = F₂(x) ; :: thesis: f1 = f2
let u be Element of F₁(); :: according to FUNCT_2:def 8 :: thesis: f1 . u = f2 . u
thus f2 . u = F₂(u) by A2
.= f1 . u by A1 ; :: thesis: verum