let L be non empty satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3 ShefferStr ; :: thesis: for z, p, y, x being Element of L holds z | (x | p) = z | (p | ((x | (y | (y | y))) | (x | (y | (y | y)))))
let z, p, y, x be Element of L; :: thesis: z | (x | p) = z | (p | ((x | (y | (y | y))) | (x | (y | (y | y)))))
(((p | p) | z) | ((x | (y | (y | y))) | z)) | (((p | p) | z) | ((x | (y | (y | y))) | z)) = z | (p | ((x | (y | (y | y))) | (x | (y | (y | y))))) by Th130;
hence z | (x | p) = z | (p | ((x | (y | (y | y))) | (x | (y | (y | y))))) by Th150; :: thesis: verum