let X be ARS ; :: thesis: for x, y being Element of X st x ==> y holds
x <<01>> y
let x, y be Element of X; :: thesis: ( x ==> y implies x <<01>> y )
assume A1: x ==> y ; :: thesis: x <<01>> y
take x ; :: according to ABSRED_0:def 22 :: thesis: ( x <=01= x & x =01=> y )
thus ( x <=01= x & x =01=> y ) by A1; :: thesis: verum