let L be non empty satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3 ShefferStr ; :: thesis: for x, p being Element of L holds (p | x) | (p | ((x | x) | (x | x))) = (((x | x) | (x | x)) | p) | (((x | x) | (x | x)) | p)
let x, p be Element of L; :: thesis: (p | x) | (p | ((x | x) | (x | x))) = (((x | x) | (x | x)) | p) | (((x | x) | (x | x)) | p)
(x | x) | (x | x) = x by SHEFFER1:def 13;
hence (p | x) | (p | ((x | x) | (x | x))) = (((x | x) | (x | x)) | p) | (((x | x) | (x | x)) | p) by SHEFFER1:def 15; :: thesis: verum