let f, g be UnOp of the carrier of F; :: thesis: ( ( for x being Element of F holds f . x = - x ) & ( for x being Element of F holds g . x = - x ) implies f = g )
assume that
A1: for x being Element of F holds f . x = - x and
A2: for x being Element of F holds g . x = - x ; :: thesis: f = g

now :: thesis: for x being object st x in the carrier of F holds
f . x = g . x

let x be object ; :: thesis: ( x in the carrier of F implies f . x = g . x )
assume x in the carrier of F ; :: thesis: f . x = g . x
then reconsider y = x as Element of F ;
thus f . x = - y by A1
.= g . x by A2 ; :: thesis: verum

end;

hence f = g by FUNCT_2:12; :: thesis: verum