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