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 | p) | (x | p)

let x, p be Element of L; :: thesis: (p | x) | (p | x) = (x | p) | (x | p)

(x | x) | (x | x) = x by SHEFFER1:def 13;

hence (p | x) | (p | x) = (x | p) | (x | p) by Th86; :: thesis: verum

let x, p be Element of L; :: thesis: (p | x) | (p | x) = (x | p) | (x | p)

(x | x) | (x | x) = x by SHEFFER1:def 13;

hence (p | x) | (p | x) = (x | p) | (x | p) by Th86; :: thesis: verum