let f1, f2 be Function of (BOOLEAN *),NAT; :: thesis: ( ( for x being Element of BOOLEAN * holds f1 . x = ExAbsval x ) & ( for x being Element of BOOLEAN * holds f2 . x = ExAbsval x ) implies f1 = f2 )
assume that
AS1: for x being Element of BOOLEAN * holds f1 . x = ExAbsval x and
AS2: for x being Element of BOOLEAN * holds f2 . x = ExAbsval x ; :: thesis: f1 = f2
for x being Element of BOOLEAN * holds f1 . x = f2 . x

proof

let x be Element of BOOLEAN * ; :: thesis: f1 . x = f2 . x
thus f1 . x = ExAbsval x by AS1
.= f2 . x by AS2 ; :: thesis: verum

end;

hence f1 = f2 by FUNCT_2:def 8; :: thesis: verum