let L be non empty satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3 ShefferStr ; :: thesis: for w, p being Element of L holds (p | p) | (p | (w | (w | w))) = ((w | w) | p) | (((w | w) | (w | w)) | p)
let w, p be Element of L; :: thesis: (p | p) | (p | (w | (w | w))) = ((w | w) | p) | (((w | w) | (w | w)) | p)
p | (w | (w | w)) = p | p by SHEFFER1:def 14;
hence (p | p) | (p | (w | (w | w))) = ((w | w) | p) | (((w | w) | (w | w)) | p) by SHEFFER1:def 15; :: thesis: verum