let L be non empty satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3 ShefferStr ; :: thesis: for p, z, y, x being Element of L holds z | (x | p) = (((p | p) | z) | ((x | (y | (y | y))) | z)) | (((p | p) | z) | ((x | (y | (y | y))) | z))
let p, z, y, x be Element of L; :: thesis: z | (x | p) = (((p | p) | z) | ((x | (y | (y | y))) | z)) | (((p | p) | z) | ((x | (y | (y | y))) | z))
((z | (x | p)) | (z | (x | p))) | (((x | (y | (y | y))) | z) | ((p | p) | z)) = z | (x | p) by Th144;
hence z | (x | p) = (((p | p) | z) | ((x | (y | (y | y))) | z)) | (((p | p) | z) | ((x | (y | (y | y))) | z)) by Th149; :: thesis: verum