let L be non empty satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3 ShefferStr ; :: thesis: for q, p, y being Element of L holds (((y | y) | y) | p) | ((q | q) | p) = (p | ((p | p) | q)) | (p | ((p | p) | q))
let q, p, y be Element of L; :: thesis: (((y | y) | y) | p) | ((q | q) | p) = (p | ((p | p) | q)) | (p | ((p | p) | q))
p | p = ((y | y) | y) | p by Th101;
hence (((y | y) | y) | p) | ((q | q) | p) = (p | ((p | p) | q)) | (p | ((p | p) | q)) by Th74; :: thesis: verum