let L be non empty satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3 ShefferStr ; :: thesis: for q, w being Element of L holds w | q = ((w | w) | (w | q)) | ((q | q) | (w | q))

now :: thesis: for y, q, w being Element of L holds w | q = ((w | w) | (w | q)) | ((q | q) | (w | q))

let y, q, w be Element of L; :: thesis: w | q = ((w | w) | (w | q)) | ((q | q) | (w | q))
((w | q) | ((y | y) | y)) | ((w | q) | (w | q)) = w | q by Th78;
hence w | q = ((w | w) | (w | q)) | ((q | q) | (w | q)) by Th88; :: thesis: verum

end;

hence for q, w being Element of L holds w | q = ((w | w) | (w | q)) | ((q | q) | (w | q)) ; :: thesis: verum