let L be non empty satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3 ShefferStr ; :: thesis: for q, p, x being Element of L holds (x | p) | ((q | q) | p) = (p | ((x | x) | q)) | (p | ((x | x) | q))
let q, p, x be Element of L; :: thesis: (x | p) | ((q | q) | p) = (p | ((x | x) | q)) | (p | ((x | x) | q))
(x | x) | (x | x) = x by SHEFFER1:def 13;
hence (x | p) | ((q | q) | p) = (p | ((x | x) | q)) | (p | ((x | x) | q)) by SHEFFER1:def 15; :: thesis: verum