let X, Y be non empty set ; for x being Element of X
for y being Element of Y holds
( ( x = y implies (Imf (X,Y)) . (x,y) = 1 ) & ( x <> y implies (Imf (X,Y)) . (x,y) = 0 ) )
let x be Element of X; for y being Element of Y holds
( ( x = y implies (Imf (X,Y)) . (x,y) = 1 ) & ( x <> y implies (Imf (X,Y)) . (x,y) = 0 ) )
let y be Element of Y; ( ( x = y implies (Imf (X,Y)) . (x,y) = 1 ) & ( x <> y implies (Imf (X,Y)) . (x,y) = 0 ) )
[x,y] in [:X,Y:]
by ZFMISC_1:87;
hence
( ( x = y implies (Imf (X,Y)) . (x,y) = 1 ) & ( x <> y implies (Imf (X,Y)) . (x,y) = 0 ) )
by Def4; verum