let f, g be Function; :: thesis: for x, y being set st dom f = dom g & f . x = g . x & f . y = g . y holds
f | {x,y} = g | {x,y}
let x, y be set ; :: thesis: ( dom f = dom g & f . x = g . x & f . y = g . y implies f | {x,y} = g | {x,y} )
assume ( dom f = dom g & f . x = g . x & f . y = g . y ) ; :: thesis: f | {x,y} = g | {x,y}
then A1: ( f | {x} = g | {x} & f | {y} = g | {y} ) by Th27;
{x,y} = {x} \/ {y} by ENUMSET1:1;
hence f | {x,y} = g | {x,y} by A1, RELAT_1:150; :: thesis: verum