Suppose we are given two axioms in Real Nos:

1) for all,x ( x+0=x)

2)for all x.y,z [ (x+y)z =xy +yz]

The equality theorem : for all ,x,y,z [ (x=y &y=z) => x=z]

The substitution law ,and

The cancellation law for addition : for all ,x,y,z [(x+y =x+z) => y=z]

Use the appropriate laws of logic to create a theorem in Real Nos