let L be non empty satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3 ShefferStr ; :: thesis: for q, p, y, w being Element of L holds ((w | (y | (y | y))) | p) | ((q | q) | p) = (p | (w | q)) | (p | (w | q))
let q, p, y, w be Element of L; :: thesis: ((w | (y | (y | y))) | p) | ((q | q) | p) = (p | (w | q)) | (p | (w | q))
w | w = w | (y | (y | y)) by SHEFFER1:def 14;
hence ((w | (y | (y | y))) | p) | ((q | q) | p) = (p | (w | q)) | (p | (w | q)) by SHEFFER1:def 15; :: thesis: verum