let X be ARS ; :: thesis: for x, y, z being Element of X st x <=01=> y & y ==> z holds
x <=+=> z
let x, y, z be Element of X; :: thesis: ( x <=01=> y & y ==> z implies x <=+=> z )
assume A1: x <=01=> y ; :: thesis: ( not y ==> z or x <=+=> z )
assume A2: y ==> z ; :: thesis: x <=+=> z
A4: y <==> z by A2;
thus x <=+=> z by A1, A4, Lem1A, Def8; :: thesis: verum