let L be non empty satisfying_Sh_1 ShefferStr ; :: thesis: for x, y, z, u being Element of L holds ((x | (y | z)) | (x | (x | (y | z)))) | ((z | ((x | z) | z)) | (u | (x | (y | z)))) = z | ((x | z) | z)
let x, y, z, u be Element of L; :: thesis: ((x | (y | z)) | (x | (x | (y | z)))) | ((z | ((x | z) | z)) | (u | (x | (y | z)))) = z | ((x | z) | z)
set Y = z | ((x | z) | z);
set X = x | (y | z);
((x | (y | z)) | (((z | ((x | z) | z)) | (x | (y | z))) | (x | (y | z)))) | ((z | ((x | z) | z)) | (u | (x | (y | z)))) = z | ((x | z) | z) by Def1;
hence ((x | (y | z)) | (x | (x | (y | z)))) | ((z | ((x | z) | z)) | (u | (x | (y | z)))) = z | ((x | z) | z) by Def1; :: thesis: verum