let L be non empty properly_defined satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3 ShefferOrthoLattStr ; :: thesis: for x, y being Element of L holds x | y = y | x
let x, y be Element of L; :: thesis: x | y = y | x
x | y = ((x | y) " ) " by Def13
.= ((x | ((y " ) " )) " ) " by Def13
.= ((((y " ) " ) | x) " ) " by Def15
.= ((y | x) " ) " by Def13
.= y | x by Def13 ;
hence x | y = y | x ; :: thesis: verum