let f, g be Function; :: thesis: for x, y, z being set st dom f = dom g & f . x = g . x & f . y = g . y & f . z = g . z holds
f | {x,y,z} = g | {x,y,z}
let x, y, z be set ; :: thesis: ( dom f = dom g & f . x = g . x & f . y = g . y & f . z = g . z implies f | {x,y,z} = g | {x,y,z} )
assume ( dom f = dom g & f . x = g . x & f . y = g . y & f . z = g . z ) ; :: thesis: f | {x,y,z} = g | {x,y,z}
then A1: ( f | {x,y} = g | {x,y} & f | {z} = g | {z} ) by Th27, Th28;
{x,y,z} = {x,y} \/ {z} by ENUMSET1:3;
hence f | {x,y,z} = g | {x,y,z} by A1, RELAT_1:150; :: thesis: verum