let x, y be ExtReal; :: thesis: for a, b being Real st x = a & y = b holds
x - y = a - b
let a, b be Real; :: thesis: ( x = a & y = b implies x - y = a - b )
assume A1: x = a ; :: thesis: ( not y = b or x - y = a - b )
assume y = b ; :: thesis: x - y = a - b
then - y = - b by XXREAL_3:def 3;
hence x - y = a - b by A1, XXREAL_3:def 2; :: thesis: verum