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