let L be non empty satisfying_Sh_1 ShefferStr ; :: thesis: for x, y, z being Element of L holds (x | (y | z)) | (x | (y | y)) = (x | (y | z)) | (x | (y | z))

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

(x | (y | z)) | ((y | x) | x) = (x | (y | z)) | (x | (y | y)) by Th43;

hence (x | (y | z)) | (x | (y | y)) = (x | (y | z)) | (x | (y | z)) by Th35; :: thesis: verum

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

(x | (y | z)) | ((y | x) | x) = (x | (y | z)) | (x | (y | y)) by Th43;

hence (x | (y | z)) | (x | (y | y)) = (x | (y | z)) | (x | (y | z)) by Th35; :: thesis: verum