a=a

The same term is on both sides of the equality sign

If a=b then b=a

It is basically switching the terms to the opposite side of the equality sign

If a=b and b=c then a=c

So it is basically cutting the middle man, b, out of the equation. As you see up there b is in the middle and a is equal to b and b is equal to c so a is therefore equal to c.

Substitution Property

If a=b then b can replace a in any expression

^^^^^

It is pretty self explanitory 

For all real numbers x,y, and z,

if x=y, then x+z=y+z

For all real numbers, x, y, and z

if x=y, then x-z=y-z

For all real numbers x, y, and z

if x=y, then xz=yz

For all real numbers, x, y, and z

if x=y and z does not equal 0

then x/z=y/z