let X, Y be set ; :: thesis: for f1, f2 being Function st dom f1 = [:X,Y:] & dom f2 = [:X,Y:] & curry' f1 = curry' f2 holds
f1 = f2
let f1, f2 be Function; :: thesis: ( dom f1 = [:X,Y:] & dom f2 = [:X,Y:] & curry' f1 = curry' f2 implies f1 = f2 )
assume that
A1: dom f1 = [:X,Y:] and
A2: dom f2 = [:X,Y:] and
A3: curry' f1 = curry' f2 ; :: thesis: f1 = f2
( dom (~ f1) = [:Y,X:] & dom (~ f2) = [:Y,X:] ) by A1, A2, FUNCT_4:46;
then A4: ~ f1 = ~ f2 by A3, Th37;
~ (~ f1) = f1 by A1, FUNCT_4:52;
hence f1 = f2 by A2, A4, FUNCT_4:52; :: thesis: verum