let X be ARS ; :: thesis: for x, y, z being Element of X st x <=+=> y & y =01=> z holds
x <=+=> z
let x, y, z be Element of X; :: thesis: ( x <=+=> y & y =01=> z implies x <=+=> z )
assume A1: x <=+=> y ; :: thesis: ( not y =01=> z or x <=+=> z )
assume A2: y =01=> z ; :: thesis: x <=+=> z
A3: y <=01=> z by A2, Lem43;
thus x <=+=> z by A1, A3, Lem18; :: thesis: verum