let L be non empty satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3 ShefferStr ; :: thesis: for p, w, q, y being Element of L holds (((y | y) | y) | q) | ((w | w) | q) = (q | (((p | (p | p)) | (p | (p | p))) | w)) | (q | (((p | (p | p)) | (p | (p | p))) | w))
let p, w, q, y be Element of L; :: thesis: (((y | y) | y) | q) | ((w | w) | q) = (q | (((p | (p | p)) | (p | (p | p))) | w)) | (q | (((p | (p | p)) | (p | (p | p))) | w))
((p | (p | p)) | (p | (p | p))) | (p | (p | p)) = (y | y) | y by Th104;
hence (((y | y) | y) | q) | ((w | w) | q) = (q | (((p | (p | p)) | (p | (p | p))) | w)) | (q | (((p | (p | p)) | (p | (p | p))) | w)) by Th73; :: thesis: verum