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

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

hence
for w, z, x being Element of L holds w | x = w | ((x | z) | (x | w))
; :: thesis: verumlet y, w, z, x be Element of L; :: thesis: w | x = w | ((x | z) | (x | w))

(x | (y | (y | y))) | (x | (y | (y | y))) = x by Th136;

hence w | x = w | ((x | z) | (x | w)) by Th155; :: thesis: verum

end;(x | (y | (y | y))) | (x | (y | (y | y))) = x by Th136;

hence w | x = w | ((x | z) | (x | w)) by Th155; :: thesis: verum