let X be ARS ; :: thesis: for x, y being Element of X st x =+=> y holds
x =*=> y
let x, y be Element of X; :: thesis: ( x =+=> y implies x =*=> y )
assume A1: x =+=> y ; :: thesis: x =*=> y
consider z being Element of X such that
A2: ( x ==> z & z =*=> y ) by A1;
A3: x =*=> z by A2, Th2;
thus x =*=> y by A2, A3, Th3; :: thesis: verum