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

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

(x | (y | y)) | (y | x) = x by Th106;

hence (y | x) | x = ((x | (y | y)) | (x | (y | y))) | (y | x) by Th119; :: thesis: verum

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

(x | (y | y)) | (y | x) = x by Th106;

hence (y | x) | x = ((x | (y | y)) | (x | (y | y))) | (y | x) by Th119; :: thesis: verum