let L be non empty satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3 ShefferStr ; :: thesis: for q, p being Element of L holds (p | p) | (p | ((q | q) | q)) = (((q | q) | (q | q)) | p) | ((q | q) | p)
let q, p be Element of L; :: thesis: (p | p) | (p | ((q | q) | q)) = (((q | q) | (q | q)) | p) | ((q | q) | p)
p | ((q | q) | q) = p | p by Th70;
hence (p | p) | (p | ((q | q) | q)) = (((q | q) | (q | q)) | p) | ((q | q) | p) by SHEFFER1:def 15; :: thesis: verum