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 that
A1: dom f = dom g and
A2: f . x = g . x and
A3: f . y = g . y ; :: thesis: f | {x,y} = g | {x,y}
A4: f | {x} = g | {x} by A1, A2, Th90;
A5: f | {y} = g | {y} by A1, A3, Th90;
{x,y} = {x} \/ {y} by ENUMSET1:41;
hence f | {x,y} = g | {x,y} by A4, A5, RELAT_1:185; :: thesis: verum