let L be non empty satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3 ShefferStr ; :: thesis: for z, w, y, x being Element of L holds w | x = w | ((x | z) | (((x | (y | (y | y))) | (x | (y | (y | y)))) | w))

let z, w, y, x be Element of L; :: thesis: w | x = w | ((x | z) | (((x | (y | (y | y))) | (x | (y | (y | y)))) | w))

(x | (y | (y | y))) | (x | z) = x by Th134;

hence w | x = w | ((x | z) | (((x | (y | (y | y))) | (x | (y | (y | y)))) | w)) by Th148; :: thesis: verum

let z, w, y, x be Element of L; :: thesis: w | x = w | ((x | z) | (((x | (y | (y | y))) | (x | (y | (y | y)))) | w))

(x | (y | (y | y))) | (x | z) = x by Th134;

hence w | x = w | ((x | z) | (((x | (y | (y | y))) | (x | (y | (y | y)))) | w)) by Th148; :: thesis: verum